saf_utility_loudspeaker_presets.c

Go to the documentation of this file.

/*
 * Copyright 2016-2018 Leo McCormack
 *
 * Permission to use, copy, modify, and/or distribute this software for any
 * purpose with or without fee is hereby granted, provided that the above
 * copyright notice and this permission notice appear in all copies.
 *
 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES WITH
 * REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY
 * AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT,
 * INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM
 * LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR
 * OTHER TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR
 * PERFORMANCE OF THIS SOFTWARE.
 */
 
#include "saf_utility_loudspeaker_presets.h"
 
/* mono */
const float __mono_dirs_deg[1][2] =
{ { 0.0f,    0.0f}};
 
/* stereo pair */
const float __stereo_dirs_deg[2][2] =
{ { 30.0f,    0.0f},
  { -30.0f,    0.0f}};
 
/* 5.X surround */
const float __5pX_dirs_deg[5][2] =
{ { 30.0f,    0.0f},
  { -30.0f,    0.0f},
  { 0.0f,    0.0f},
  { 110.0f,    0.0f},
  { -110.0f,    0.0f}};
 
/* 7.X surround */
const float __7pX_dirs_deg[7][2] =
{ { 30.0f,    0.0f},
  { -30.0f,    0.0f},
  { 0.0f,    0.0f},
  { 90.0f,    0.0f},
  { -90.0f,    0.0f},
  { 135.0f,    0.0f},
  { -135.0f,    0.0f}};
 
/* 8.X surround */
const float __8pX_dirs_deg[8][2] =
{ { 30.0f,    0.0f},
  { -30.0f,    0.0f},
  { 110.0f,    0.0f},
  { -110.0f,    0.0f},
  { 30.0f,    45.0f},
  { -30.0f,    45.0f},
  { 110.0f,    45.0f},
  { -110.0f,    45.0f}};
 
/* 9.X surround */
const float __9pX_dirs_deg[9][2] =
{ { 30.0f,    0.0f},
  { -30.0f,    0.0f},
  { 0.0f,    0.0f},
  { 110.0f,    0.0f},
  { -110.0f,    0.0f},
  { 30.0f,    45.0f},
  { -30.0f,    45.0f},
  { 110.0f,    45.0f},
  { -110.0f,    45.0f}};
 
/* 10.X surround */
const float __10pX_dirs_deg[10][2] =
{ { 30.0f,    0.0f},
  { -30.0f,    0.0f},
  { 0.0f,    0.0f},
  { 110.0f,    0.0f},
  { -110.0f,    0.0f},
  { 30.0f,    45.0f},
  { -30.0f,    45.0f},
  { 0.0f,    90.0f},
  { 110.0f,    45.0f},
  { -110.0f,    45.0f}};
 
/* 11.X surround */
const float __11pX_dirs_deg[11][2] =
{ { 30.0f,    0.0f},
  { -30.0f,    0.0f},
  { 0.0f,    0.0f},
  { 110.0f,    0.0f},
  { -110.0f,    0.0f},
  { 30.0f,    45.0f},
  { -30.0f,    45.0f},
  { 0.0f,    45.0f},
  { 0.0f,    90.0f},
  { 110.0f,    45.0f},
  { -110.0f,    45.0f}};
 
/* 11.X (7+4) surround */
const float __11pX_7_4_dirs_deg[11][2] =
{ { 30.0f,    0.0f},
  { -30.0f,    0.0f},
  { 0.0f,    0.0f},
  { 110.0f,    0.0f},
  { -110.0f,    0.0f},
  { 135.0f,    0.0f},
  { -135.0f,    0.0f},
  { 30.0f,    45.0f},
  { -30.0f,    45.0f},
  { 110.0f,    45.0f},
  { -110.0f,    45.0f}};
 
/* 13.X surround */
const float __13pX_dirs_deg[13][2] =
{ { 30.0f,    0.0f},
  { -30.0f,    0.0f},
  { 0.0f,    0.0f},
  { 90.0f,    0.0f},
  { -90.0f,    0.0f},
  { 135.0f,    0.0f},
  { -135.0f,    0.0f},
  { 30.0f,    45.0f},
  { -30.0f,    45.0f},
  { 0.0f,    45.0f},
  { 0.0f,    90.0f},
  { 90.0f,    45.0f},
  { -90.0f,    45.0f}};
 
/* 22.X surround */
const float __22pX_dirs_deg[22][2] =
{ { 45.0f,    0.0f},
  { -45.0f,    0.0f},
  { 0.0f,    0.0f},
  { 135.0f,    0.0f},
  { -135.0f,    0.0f},
  { 15.0f,    0.0f},
  { -15.0f,    0.0f},
  { 90.0f,    0.0f},
  { -90.0f,    0.0f},
  { 180.0f,    0.0f},
  { 45.0f,    45.0f},
  { -45.0f,    45.0f},
  { 0.0f,    45.0f},
  { 135.0f,    45.0f},
  { -135.0f,    45.0f},
  { 90.0f,    45.0f},
  { -90.0f,    45.0f},
  { 180.0f,    45.0f},
  { 0.0f,    90.0f},
  { 45.0f,    -30.0f},
  { -45.0f,    -30.0f},
  { 0.0f,    -30.0f}};
 
/* 9+10+3 */
const float __9_10_3p2_dirs_deg[24][2] =
{ { 45.0f,     0.0f},
  { -45.0f,     0.0f},
  { 0.0f,     0.0f},
  { 30.0f,     -15.0f},
  { 110.0f,     0.0f},
  { -110.0f,     0.0f},
  { 22.5f,     0.0f},
  { -22.5f,     0.0f},
  { 180.0f,     0.0f},
  { -30.0f,     -15.0f},
  { 90.0f,     0.0f},
  { -90.0f,     0.0f},
  { 45.0f,     30.0f},
  { -45.0f,     30.0f},
  { 0.0f,     30.0f},
  { 0.0f,     90.0f},
  { 110.0f,     30.0f},
  { -110.0f,     30.0f},
  { 90.0f,     30.0f},
  { -90.0f,     30.0f},
  { 180.0f,     30.0f},
  { 0.0f,     -15.0f},
  { 45.0f,     -15.0f},
  { -45.0f,     -15.0f}};
 
/* Aalto MCC */
const float __Aalto_MCC_dirs_deg[45][2] =
{ { 120.0f,     0.0f},
  { 90.0f,     0.0f},
  { 75.0f,     0.0f},
  { 60.0f,     0.0f},
  { 45.0f,     0.0f},
  { 30.0f,     0.0f},
  { 15.0f,     0.0f},
  { 0.0f,     0.0f},
  { -15.0f,    0.0f},
  { -30.0f,    0.0f},
  { -45.0f,    0.0f},
  { -60.0f,    0.0f},
  { 135.0f,    -30.0f},
  { 45.0f,    -30.0f},
  { 0.0f,    -30.0f},
  { 0.0f,    -15.0f},
  { 0.0f,     -60.0f},
  { 90.0f,     -60.0f},
  { 135.0f,     30.0f},
  { 90.0f,     30.0f},
  { 45.0f,     30.0f},
  { 90.0f,     -30.0f},
  { 0.0f,    30.0f},
  { 0.0f,    15.0f},
  { -45.0f,    30.0f},
  { -90.0f,    30.0f},
  { 0.0f,    60.0f},
  { 90.0f,    60.0f},
  { 0.0f,    90.0f},
  { -90.0f,    60.0f},
  { -75.0f,     0.0f},
  { -90.0f,     0.0f},
  { -120.0f,     0.0f},
  { -150.0f,    0.0f},
  { 180.0f,    0.0f},
  { 150.0f,    0.0f},
  { -45.0f,    -30.0f},
  { -135.0f,    -30.0f},
  { 180.0f,    -30.0f},
  { -90.0f,     -60.0f},
  { -90.0f,     30.0f},
  { -135.0f,     30.0f},
  { 180.0f,    30.0f},
  { 180.0f,    60.0f},
  { 180.0f,    -60.0f}};
 
const float __Aalto_MCCsubset_dirs_deg[37][2] = 
{ { 0.0f,     90.0f},
  { 0.0f,     60.0f},
  { 90.0f,     60.0f},
  { 180.0f,     60.0f},
  { -90.0f,     60.0f},
  { 0.0f,     30.0f},
  { 45.0f,     30.0f},
  { 90.0f,     0.0f},
  { 135.0f,     30.0f},
  { 180.0f,     30.0f},
  { -135.0f,     30.0f},
  { -90.0f,     30.0f},
  { -45.0f,     30.0f},
  { 0.0f,     0.0f},
  { 30.0f,     0.0f},
  { 60.0f,     0.0f},
  { 90.0f,     0.0f},
  { 120.0f,     0.0f},
  { 150.0f,     0.0f},
  { 180.0f,     0.0f},
  { -150.0f,     0.0f},
  { -120.0f,     0.0f},
  { -90.0f,     0.0f},
  { -60.0f,     0.0f},
  { -30.0f,     0.0f},
  { 0.0f,     -30.0f},
  { 45.0f,     -30.0f},
  { 90.0f,     -30.0f},
  { 135.0f,     -30.0f},
  { 180.0f,     -30.0f},
  { -135.0f,     -30.0f},
  { -90.0f,     -30.0f},
  { -45.0f,     -30.0f},
  { 0.0f,     -60.0f},
  { 90.0f,     -60.0f},
  { 180.0f,     -60.0f},
  { -90.0f,     -60.0}};
 
/* Aalto Apaja */
const float __Aalto_Apaja_dirs_deg[29][2] =
{ { 18.0f,     0.0f},
  { 54.0f,     0.0f},
  { 90.0f,     0.0f},
  { 126.0f,     0.0f},
  { 166.0f,     0.0f},
  { -166.0f,     0.0f},
  { -126.0f,     0.0f},
  { -90.0f,     0.0f},
  { -54.0f,     0.0f},
  { -18.0f,     0.0f},
  { 18.0f,    -25.0f},
  { 54.0f,    -25.0f},
  { 90.0f,    -25.0f},
  { 144.0f,    -25.0f},
  { -144.0f,    -25.0f},
  { -90.0f,    -25.0f},
  { -54.0f,    -25.0f},
  { -18.0f,    -25.0f},
  { 18.0f,    25.0f},
  { 54.0f,    25.0f},
  { 90.0f,    25.0f},
  { -90.0f,    25.0f},
  { -54.0f,    25.0f},
  { -18.0f,    25.0f},
  { 40.0f,    45.0f},
  { 137.0f,    45.0f},
  { -137.0f,    45.0f},
  { -40.0f,    45.0f},
  { 0.0f,    90.0f}};
 
/* Aalto listening room */
const float __Aalto_LR_dirs_deg[13][2] =
{ { 30.0f,     0.0f},
  { -30.0f,     0.0f},
  { 0.0f,     0.0f},
  { 70.0f,     0.0f},
  { 110.0f,     0.0f},
  { -70.0f,     0.0f},
  { -110.0f,     0.0f},
  { 160.0f,     0.0f},
  { -160.0f,     0.0f},
  { 45.0f,    45.0f},
  { 135.0f,    45.0f},
  { -45.0f,    45.0f},
  { -135.0f,    45.0f}};
 
/* DTU AVIL */
const float __DTU_AVIL_dirs_deg[64][2] =
{ { 0.0f,    80.0f},
  { -180.0f,    80.0f},
  { 0.0f,    56.0f},
  { 60.0f,    56.0f},
  { 120.0f,    56.0f},
  { -180.0f,    56.0f},
  { -120.0f,    56.0f},
  { -60.0f,    56.0f},
  { 0.0f,    28.0f},
  { 30.0f,    28.0f},
  { 60.0f,    28.0f},
  { 90.0f,    28.0f},
  { 120.0f,    28.0f},
  { 150.0f,    28.0f},
  { -180.0f,    28.0f},
  { -150.0f,    28.0f},
  { -120.0f,    28.0f},
  { -90.0f,    28.0f},
  { -60.0f,    28.0f},
  { -30.0f,    28.0f},
  { 0.0f,     0.0f},
  { 15.0f,    0.0f},
  { 30.0f,    0.0f},
  { 45.0f,    0.0f},
  { 60.0f,    0.0f},
  { 75.0f,    0.0f},
  { 90.0f,    0.0f},
  { 105.0f,    0.0f},
  { 120.0f,    0.0f},
  { 135.0f,    0.0f},
  { 150.0f,    0.0f},
  { 165.0f,    0.0f},
  { -180.0f,    0.0f},
  { -165.0f,    0.0f},
  { -150.0f,    0.0f},
  { -135.0f,    0.0f},
  { -120.0f,    0.0f},
  { -105.0f,    0.0f},
  { -90.0f,    0.0f},
  { -75.0f,    0.0f},
  { -60.0f,    0.0f},
  { -45.0f,    0.0f},
  { -30.0f,    0.0f},
  { -15.0f,    0.0f},
  { 0.0f,    -28.0f},
  { 30.0f,    -28.0f},
  { 60.0f,    -28.0f},
  { 90.0f,    -28.0f},
  { 120.0f,    -28.0f},
  { 150.0f,    -28.0f},
  { -180.0f,    -28.0f},
  { -150.0f,    -28.0f},
  { -120.0f,    -28.0f},
  { -90.0f,    -28.0f},
  { -60.0f,    -28.0f},
  { -30.0f,    -28.0f},
  { 30.0f,    -56.0f},
  { 90.0f,    -56.0f},
  { 150.0f,    -56.0f},
  { -150.0f,    -56.0f},
  { -90.0f,    -56.0f},
  { -30.0f,    -56.0f},
  { 90.0f,    -80.0f},
  { -90.0f,    -80.0f}};
 
/* Zylia Lab */
const float __Zylia_Lab_dirs_deg[22][2] =
{ { 45.0f,    0.0f},
  { -45.0f,    0.0f},
  { 0.0f,    0.0f},
  { 135.0f,    0.0f},
  { -135.0f,    0.0f},
  { 30.0f,    0.0f},
  { -30.0f,    0.0f},
  { -180.0f,    0.0f},
  { 90.0f,    0.0f},
  { -90.0f,    0.0f},
  { 45.0f,    30.0f},
  { -45.0f,    30.0f},
  { 0.0f,    30.0f},
  { 0.0f,    90.0f},
  { 135.0f,    30.0f},
  { -135.0f,    30.0f},
  { 90.0f,    30.0f},
  { -90.0f,    30.0f},
  { 180.0f,    30.0f},
  { 0.0f,    -25.0f},
  { 45.0f,    -25.0f},
  { -45.0f,    -25.0f}};
 
/* 64 point sphere-covering (IN RADIANS!) */
const float __default_LScoords64_rad[64][2] =
{ { 0.0f,     1.57079632679490f},
  { 2.39996322972865f,     1.31814860051033f},
  { -1.48325884772228f,     1.21253510828228f},
  { 0.916704382006374f,     1.13082037200398f},
  { -2.96651769544456f,     1.06135247798300f},
  { -0.566554465715905f,     0.999627828229359f},
  { 1.83340876401275f,     0.943340553871706f},
  { -2.04981331343819f,     0.891122507886653f},
  { 0.350149916290469f,     0.842082876051491f},
  { 2.75011314601912f,     0.795602953484535f},
  { -1.13310893143181f,     0.751231999126636f},
  { 1.26685429829684f,     0.708629271562384f},
  { -2.61636777915409f,     0.667529444635833f},
  { -0.216404549425435f,     0.627720817657913f},
  { 2.18355868030321f,     0.589030970216274f},
  { -1.69966339714772f,     0.551316969131883f},
  { 0.700299832580937f,     0.514458475561187f},
  { 3.10026306230959f,     0.478352764649258f},
  { -0.782959015141339f,     0.442911044073639f},
  { 1.61700421458731f,     0.408055677301279f},
  { -2.26621786286362f,     0.373718050942914f},
  { 0.133745366865034f,     0.339836909454122f},
  { 2.53370859659368f,     0.306357034556919f},
  { -1.34951348085725f,     0.273228182540638f},
  { 1.05044974887141f,     0.240404216769259f},
  { -2.83277232857953f,     0.207842389353347f},
  { -0.432809098850870f,     0.175502737575723f},
  { 1.96715413087779f,     0.143347568905365f},
  { -1.91606794657316f,     0.111341014340964f},
  { 0.483895283155495f,     0.0794486340851373f},
  { 2.88385851288415f,     0.0476370626244032f},
  { -0.999363564566781f,     0.0158736824899558f},
  { 1.40059966516187f,     -0.0158736824899556f},
  { -2.48262241228906f,     -0.0476370626244031f},
  { -0.0826591825604016f,     -0.0794486340851372f},
  { 2.31730404716825f,     -0.111341014340964f},
  { -1.56591803028268f,     -0.143347568905365f},
  { 0.834045199445964f,     -0.175502737575723f},
  { -3.04917687800497f,     -0.207842389353347f},
  { -0.649213648276312f,     -0.240404216769259f},
  { 1.75074958145234f,     -0.273228182540638f},
  { -2.13247249599859f,     -0.306357034556919f},
  { 0.267490733730067f,     -0.339836909454122f},
  { 2.66745396345872f,     -0.373718050942914f},
  { -1.21576811399222f,     -0.408055677301278f},
  { 1.18419511573643f,     -0.442911044073639f},
  { -2.69902696171450f,     -0.478352764649258f},
  { -0.299063731985844f,     -0.514458475561187f},
  { 2.10089949774281f,     -0.551316969131883f},
  { -1.78232257970812f,     -0.589030970216274f},
  { 0.617640650020536f,     -0.627720817657913f},
  { 3.01760387974919f,     -0.667529444635833f},
  { -0.865618197701740f,     -0.708629271562384f},
  { 1.53434503202690f,     -0.751231999126636f},
  { -2.34887704542402f,     -0.795602953484536f},
  { 0.0510861843046390f,     -0.842082876051491f},
  { 2.45104941403327f,     -0.891122507886652f},
  { -1.43217266341767f,     -0.943340553871706f},
  { 0.967790566310990f,     -0.999627828229359f},
  { -2.91543151113994f,     -1.06135247798300f},
  { -0.515468281411286f,     -1.13082037200398f},
  { 1.88449494831737f,     -1.21253510828228f},
  { -1.99872712913356f,     -1.31814860051033f},
  { 0.401236100595093f,     -1.57079632679490f}};
 
/* Minimum T-design of degree 1 (2 points) */
const float __Tdesign_degree_1_dirs_deg[2][2] =
{ { 0.0f,    0.0f},
  { 180.0f,    0.0f}};
 
/* Minimum T-design of degree 2 (4 points) */
const float __Tdesign_degree_2_dirs_deg[4][2] =
{ { 45.0f,    35.2643896827547f},
  { -45.0f,    -35.2643896827547f},
  { 135.0f,    -35.2643896827547f},
  { -135.0f,    35.2643896827547f}};
 
/* Minimum T-design of degree 3 (6 points) */
const float __Tdesign_degree_3_dirs_deg[6][2] =
{ { 0.0f,    0.0f},
  { 180.0f,    0.0f},
  { 90.0f,    0.0f},
  { -90.0f,    0.0f},
  { 0.0f,    90.0f},
  { 0.0f,    -90.0f}};
 
/* Minimum T-design of degree 4 (12 points) */
const float __Tdesign_degree_4_dirs_deg[12][2] =
{ { 0.0f,   -31.7174744114557f},
  { -58.2825255885443f,    0.0f},
  { -90.0f,    58.2825255885443f},
  { 0.0f,    31.7174744114557f},
  { -121.717474411456f,    0.0f},
  { 90.0f,    -58.2825255885443f},
  { 180.0f,    -31.7174744114557f},
  { 121.717474411456f,    0.0f},
  { 90.0f,    58.2825255885443f},
  { 180.0f,    31.7174744114557f},
  { 58.2825255885443f,    0.0f},
  { -90.0f,    -58.2825255885443f}};
 
/* Minimum T-design of degree 5 (12 points) */
const float __Tdesign_degree_5_dirs_deg[12][2] =
{ { 0.0f,    -31.7174744114557f},
  { -58.2825255885443f,    0.0f},
  { -90.0f,    58.2825255885443f},
  { 0.0f,    31.7174744114557f},
  { -121.717474411456f,    0.0f},
  { 90.0f,    -58.2825255885443f},
  { 180.0f,    -31.7174744114557f},
  { 121.717474411456f,    0.0f},
  { 90.0f,    58.2825255885443f},
  { 180.0f,    31.7174744114557f},
  { 58.2825255885443f,    0.0f},
  { -90.0f,    -58.2825255885443f}};
 
/* Minimum T-design of degree 6 (24 points) */
const float __Tdesign_degree_6_dirs_deg[24][2] =
{ { 26.0011675216559f,    15.4641512961471f},
  { -26.0011675216559f,    -15.4641512961471f},
  { 17.1086452559122f,    -24.9937030546433f},
  { -17.1086452559122f,    24.9937030546433f},
  { 153.998832478344f,    -15.4641512961471f},
  { -153.998832478344f,    15.4641512961471f},
  { 162.891354744088f,    24.9937030546433f},
  { -162.891354744088f,    -24.9937030546433f},
  { 72.8913547440879f,    24.9937030546433f},
  { 107.108645255912f,    -24.9937030546433f},
  { 116.001167521656f,    15.4641512961471f},
  { 63.9988324783441f,    -15.4641512961471f},
  { -107.108645255912f,    24.9937030546433f},
  { -72.8913547440879f,    -24.9937030546433f},
  { -63.9988324783441f,    15.4641512961471f},
  { -116.001167521656f,    -15.4641512961471f},
  { 32.2544599366034f,    60.0253819510733f},
  { -147.745540063397f,    60.0253819510733f},
  { -57.7455400633966f,    60.0253819510733f},
  { 122.254459936603f,    60.0253819510733f},
  { -32.2544599366034f,    -60.0253819510733f},
  { 147.745540063397f,    -60.0253819510733f},
  { 57.7455400633966f,    -60.0253819510733f},
  { -122.254459936603f,    -60.0253819510733f}};
 
/* Minimum T-design of degree 7 (24 points) */
const float __Tdesign_degree_7_dirs_deg[24][2] =
{ { 26.0011675216559f,    15.4641512961471f},
  { -26.0011675216559f,    -15.4641512961471f},
  { 17.1086452559122f,    -24.9937030546433f},
  { -17.1086452559122f,    24.9937030546433f},
  { 153.998832478344f,    -15.4641512961471f},
  { -153.998832478344f,    15.4641512961471f},
  { 162.891354744088f,    24.9937030546433f},
  { -162.891354744088f,    -24.9937030546433f},
  { 72.8913547440879f,    24.9937030546433f},
  { 107.108645255912f,    -24.9937030546433f},
  { 116.001167521656f,    15.4641512961471f},
  { 63.9988324783441f,    -15.4641512961471f},
  { -107.108645255912f,    24.9937030546433f},
  { -72.8913547440879f,    -24.9937030546433f},
  { -63.9988324783441f,    15.4641512961471f},
  { -116.001167521656f,    -15.4641512961471f},
  { 32.2544599366034f,    60.0253819510733f},
  { -147.745540063397f,    60.0253819510733f},
  { -57.7455400633966f,    60.0253819510733f},
  { 122.254459936603f,    60.0253819510733f},
  { -32.2544599366034f,    -60.0253819510733f},
  { 147.745540063397f,    -60.0253819510733f},
  { 57.7455400633966f,    -60.0253819510733f},
  { -122.254459936603f,    -60.0253819510733f}};
 
/* Minimum T-design of degree 8 (36 points) */
const float __Tdesign_degree_8_dirs_deg[36][2] =
{ { -31.1058979072627f,    53.6513674205628f},
  { 110.815389050019f,    30.4958163263089f},
  { 148.894102092737f,    53.6513674205628f},
  { 32.2138500404991f,    -17.8303741454541f},
  { 69.1846109499806f,    -30.4958163263089f},
  { -32.2138500404991f,    17.8303741454541f},
  { -69.1846109499805f,    30.4958163263088f},
  { -147.786149959501f,    -17.8303741454541f},
  { -110.815389050020f,    -30.4958163263088f},
  { 147.786149959501f,    17.8303741454541f},
  { 31.1058979072626f,    -53.6513674205628f},
  { -148.894102092737f,    -53.6513674205628f},
  { -21.2458891990563f,    -47.7753220046865f},
  { -108.204102998351f,    38.7823473661649f},
  { 158.754110800944f,    -47.7753220046865f},
  { 139.773839008605f,    -14.0948465161603f},
  { -71.7958970016493f,    -38.7823473661649f},
  { -139.773839008605f,    14.0948465161603f},
  { 71.7958970016493f,    38.7823473661649f},
  { -40.2261609913953f,    -14.0948465161603f},
  { 108.204102998351f,    -38.7823473661649f},
  { 40.2261609913953f,    14.0948465161603f},
  { 21.2458891990563f,    47.7753220046865f},
  { -158.754110800944f,    47.7753220046865f},
  { 106.650497293011f,    -2.55185592464980f},
  { -2.66337948016217f,    -16.6335052481040f},
  { -73.3495027069895f,    -2.55185592464980f},
  { -98.8410299750320f,    73.1605627016104f},
  { -177.336620519838f,    16.6335052481040f},
  { 98.8410299750322f,    -73.1605627016104f},
  { 177.336620519838f,    -16.6335052481040f},
  { 81.1589700249678f,    73.1605627016104f},
  { 2.66337948016217f,    16.6335052481040f},
  { -81.1589700249678f,    -73.1605627016104f},
  { -106.650497293011f,    2.55185592464980f},
  { 73.3495027069895f,    2.55185592464980f}};
 
/* Minimum T-design of degree 9 (48 points) */
const float __Tdesign_degree_9_dirs_deg[48][2] =
{ { 20.7458095293620f,    -3.55196449756749f},
  { -20.7458095293620f,    3.55196449756749f},
  { -3.79754064134731f,    -20.7041249340221f},
  { 3.79754064134731f,    20.7041249340221f},
  { 159.254190470638f,    3.55196449756749f},
  { -159.254190470638f,    -3.55196449756749f},
  { -176.202459358653f,    20.7041249340221f},
  { 176.202459358653f,    -20.7041249340221f},
  { 93.7975406413473f,    20.7041249340221f},
  { 86.2024593586527f,    -20.7041249340221f},
  { 110.745809529362f,    -3.55196449756749f},
  { 69.2541904706380f,    3.55196449756749f},
  { -86.2024593586527f,    20.7041249340221f},
  { -93.7975406413473f,    -20.7041249340221f},
  { -69.2541904706380f,    -3.55196449756749f},
  { -110.745809529362f,    3.55196449756749f},
  { -9.93943655954546f,    68.9655356143243f},
  { 170.060563440455f,    68.9655356143243f},
  { -99.9394365595455f,    68.9655356143243f},
  { 80.0605634404545f,    68.9655356143243f},
  { 9.93943655954546f,    -68.9655356143243f},
  { -170.060563440455f,    -68.9655356143243f},
  { 99.9394365595455f,    -68.9655356143243f},
  { -80.0605634404545f,    -68.9655356143243f},
  { 42.1472502314589f,    17.5681548413340f},
  { -42.1472502314589f,    -17.5681548413340f},
  { 23.1237609836156f,    -39.7724420378712f},
  { -23.1237609836156f,    39.7724420378712f},
  { 137.852749768541f,    -17.5681548413340f},
  { -137.852749768541f,    17.5681548413340f},
  { 156.876239016384f,    39.7724420378712f},
  { -156.876239016384f,    -39.7724420378712f},
  { 66.8762390163844f,    39.7724420378712f},
  { 113.123760983616f,    -39.7724420378712f},
  { 132.147250231459f,    17.5681548413340f},
  { 47.8527497685411f,    -17.5681548413340f},
  { -113.123760983616f,    39.7724420378712f},
  { -66.8762390163844f,    -39.7724420378712f},
  { -47.8527497685411f,    17.5681548413340f},
  { -132.147250231459f,    -17.5681548413340f},
  { 25.2587207267662f,    44.9785247162095f},
  { -154.741279273234f,    44.9785247162095f},
  { -64.7412792732338f,    44.9785247162095f},
  { 115.258720726766f,    44.9785247162095f},
  { -25.2587207267662f,    -44.9785247162095f},
  { 154.741279273234f,    -44.9785247162095f},
  { 64.7412792732338f,    -44.9785247162095f},
  { -115.258720726766f,    -44.9785247162095f}};
 
/* Minimum T-design of degree 10 (60 points) */
const float __Tdesign_degree_10_dirs_deg[60][2] =
{ { 144.086488857244f,    -21.4458167943600f},
  { -33.8100172036462f,    -48.9231262881892f},
  { -35.9135111427562f,    -21.4458167943601f},
  { -115.874264298536f,    33.0897377259147f},
  { -146.189982796354f,    48.9231262881893f},
  { 115.874264298536f,    -33.0897377259147f},
  { 146.189982796354f,    -48.9231262881893f},
  { 64.1257357014642f,    33.0897377259148f},
  { 33.8100172036461f,    48.9231262881892f},
  { -64.1257357014642f,    -33.0897377259147f},
  { -144.086488857244f,    21.4458167943600f},
  { 35.9135111427562f,    21.4458167943600f},
  { -45.5257844715611f,    1.95356582377390f},
  { 177.263270291625f,    44.4415290143179f},
  { 134.474215528439f,    1.95356582377390f},
  { 87.2126547494995f,    -45.4918765044616f},
  { 2.73672970837549f,    -44.4415290143179f},
  { -87.2126547494994f,    45.4918765044617f},
  { -2.73672970837557f,    44.4415290143178f},
  { -92.7873452505006f,    -45.4918765044617f},
  { -177.263270291625f,    -44.4415290143179f},
  { 92.7873452505006f,    45.4918765044617f},
  { 45.5257844715611f,    -1.95356582377396f},
  { -134.474215528439f,    -1.95356582377396f},
  { 15.5857325914359f,    -73.3350170374203f},
  { -85.4016616760217f,    16.0353405554795f},
  { -164.414267408564f,    -73.3350170374203f},
  { 163.915552255786f,    4.41906100711915f},
  { -94.5983383239783f,    -16.0353405554795f},
  { -163.915552255786f,    -4.41906100711904f},
  { 94.5983383239784f,    16.0353405554796f},
  { -16.0844477442143f,    4.41906100711910f},
  { 85.4016616760218f,    -16.0353405554795f},
  { 16.0844477442145f,    -4.41906100711915f},
  { -15.5857325914359f,    73.3350170374202f},
  { 164.414267408564f,    73.3350170374204f},
  { -60.0247824185970f,    25.2687130564713f},
  { 151.413274180519f,    26.8604557126932f},
  { 119.975217581403f,    25.2687130564713f},
  { 46.6267878204903f,    -51.5688772343955f},
  { 28.5867258194805f,    -26.8604557126932f},
  { -46.6267878204902f,    51.5688772343955f},
  { -28.5867258194805f,    26.8604557126931f},
  { -133.373212179510f,    -51.5688772343955f},
  { -151.413274180520f,    -26.8604557126932f},
  { 133.373212179510f,    51.5688772343955f},
  { 60.0247824185970f,    -25.2687130564714f},
  { -119.975217581403f,    -25.2687130564713f},
  { -109.941626532878f,    6.91123181401059f},
  { 172.652618018678f,    -19.7906490831313f},
  { 70.0583734671221f,    6.91123181401071f},
  { -70.4350022017499f,    -68.9408617534649f},
  { 7.34738198132191f,    19.7906490831313f},
  { 70.4350022017499f,    68.9408617534649f},
  { -7.34738198132179f,    -19.7906490831314f},
  { 109.564997798250f,    -68.9408617534649f},
  { -172.652618018678f,    19.7906490831314f},
  { -109.564997798250f,    68.9408617534649f},
  { 109.941626532878f,    -6.91123181401059f},
  { -70.0583734671221f,    -6.91123181401053f}};
 
/* Minimum T-design of degree 11 (70 points) */
const float __Tdesign_degree_11_dirs_deg[70][2] =
{ { 132.927291884332f,    7.69254738757899f},
  { -83.9349499672527f,    -23.7300652200871f},
  { 8.47410038634525f,    23.5127556185301f},
  { -113.340833834572f,    70.4225940747938f},
  { -103.265909909537f,    -9.89694439538752f},
  { -33.2370360923825f,    -70.7513316063095f},
  { 21.8564347471830f,    -26.4618527647561f},
  { -156.539486489880f,    47.7764936689044f},
  { -64.2647531387317f,    -7.72047049524459f},
  { 165.779530068738f,    44.5343602375216f},
  { -25.2028339893249f,    26.3897904767450f},
  { -97.0037973959711f,    -44.6578850137166f},
  { 27.8546391256925f,    9.76703456924600f},
  { 153.214218975132f,    -47.7053318175498f},
  { -155.061608694663f,    7.45302934155972f},
  { -11.8421354925543f,    -23.5901209534773f},
  { 80.5387312016125f,    23.7194484034707f},
  { -42.0561606270165f,    70.4382693912270f},
  { -31.2233262205060f,    -9.83541588740259f},
  { 38.8379041944063f,    -70.4980825105727f},
  { 93.7606877469492f,    -26.2949218109204f},
  { -84.7560200078398f,    47.6148028805222f},
  { 7.75536818082863f,    -7.51718499746626f},
  { -122.276883381108f,    44.2862347125773f},
  { 46.8012705252113f,    26.6442619674660f},
  { -24.7686335284573f,    -44.5693707254340f},
  { 99.8904719062334f,    9.91271928508000f},
  { -134.783996960185f,    -47.9599550372574f},
  { -83.0880230164493f,    7.29679922953795f},
  { 60.1281736000420f,    -23.3445981426306f},
  { 152.644656278084f,    23.6415261666079f},
  { 29.7576658909417f,    70.6843143997832f},
  { 40.7793187974476f,    -9.58140351749889f},
  { 110.183927562412f,    -70.3934534122902f},
  { 165.652065916454f,    -26.4258159091605f},
  { -12.9926632105736f,    47.7510668062369f},
  { 79.7359893585681f,    -7.30853603036844f},
  { -50.5245271190884f,    44.2632768570349f},
  { 118.923930267733f,    26.7140614474957f},
  { 47.2202861862577f,    -44.3149733480527f},
  { 171.925276523721f,    9.75899721561506f},
  { -62.5145800558502f,    -48.0361913333593f},
  { -11.1156697680531f,    7.43965099805872f},
  { 132.018041099963f,    -23.3326075548841f},
  { -135.355486412425f,    23.3868959687598f},
  { 102.370921576708f,    70.8219078016791f},
  { 112.739282398012f,    -9.48596399169388f},
  { -178.304963670831f,    -70.5801867828491f},
  { -122.319932198534f,    -26.6740262349265f},
  { 59.0763464570905f,    47.9978414043199f},
  { 151.704200334501f,    -7.38276167631068f},
  { 21.3763364190503f,    44.4970603752708f},
  { -169.005476417779f,    26.5024990214418f},
  { 118.980811786769f,    -44.2461913308458f},
  { -116.089295979010f,    9.51845076548334f},
  { 9.64767870353308f,    -47.8281351088411f},
  { 60.8933243657771f,    7.68427447425834f},
  { -156.021526862757f,    -23.5706842106942f},
  { -63.4602993325163f,    23.3074499244045f},
  { 174.929787427393f,    70.6586472132300f},
  { -175.288768596346f,    -9.68088860263008f},
  { -105.951907934032f,    -70.8026785673948f},
  { -50.1928304519800f,    -26.6963451935976f},
  { 131.358266702971f,    48.0136296461397f},
  { -136.296815007542f,    -7.63734823159200f},
  { 93.5644603506407f,    44.6651234222196f},
  { -97.0840116473627f,    26.3023490002159f},
  { -169.158278888619f,    -44.4576351865647f},
  { -44.1323835471345f,    9.52341455917443f},
  { 81.4795403841382f,    -47.6242211091394f}};
 
/* Minimum T-design of degree 12 (84 points) */
const float __Tdesign_degree_12_dirs_deg[84][2] =
{ { -154.471854278240f,    7.90217308341494f},
  { 162.147490498404f,    -63.3553431389084f},
  { 25.5281457217257f,    7.90217307936515f},
  { -81.2554874853320f,    -25.2685910920330f},
  { 17.8525094920942f,    63.3553431383131f},
  { 81.2554874704586f,    25.2685910914935f},
  { -17.8525095073670f,    -63.3553431416872f},
  { 98.7445125165515f,    -25.2685910933493f},
  { -162.147490509394f,    63.3553431422790f},
  { -98.7445125279264f,    25.2685910939373f},
  { 154.471854265406f,    -7.90217308016803f},
  { -25.5281457350890f,    -7.90217308261847f},
  { 1.29947714901319f,    -10.4733705479448f},
  { -83.0059666491382f,    79.4472145506146f},
  { -178.700522850663f,    -10.4733705444250f},
  { 100.476005172511f,    1.27782359434127f},
  { -96.9940333623604f,    -79.4472145487100f},
  { -100.476005185653f,    -1.27782359370633f},
  { 96.9940333304727f,    79.4472145491341f},
  { -79.5239948274546f,    1.27782359558816f},
  { 83.0059666551207f,    -79.4472145510240f},
  { 79.5239948144318f,    -1.27782359617381f},
  { -1.29947716210305f,    10.4733705444298f},
  { 178.700522837562f,    10.4733705478752f},
  { 157.241693353358f,    13.1533445898284f},
  { 31.1357511222634f,    -63.8901573764588f},
  { -22.7583066459503f,    13.1533445871984f},
  { -75.7795388656139f,    22.1291502833803f},
  { 148.864248861286f,    63.8901573754847f},
  { 75.7795388539796f,    -22.1291502841989f},
  { -148.864248878128f,    -63.8901573724759f},
  { 104.220461132715f,    22.1291502824035f},
  { -31.1357511316254f,    63.8901573733956f},
  { -104.220461147326f,    -22.1291502815231f},
  { -157.241693366750f,    -13.1533445864770f},
  { 22.7583066331656f,    -13.1533445905536f},
  { 110.436905260280f,    -60.6153505191573f},
  { -62.1805578014362f,    -9.86516586433484f},
  { -69.5630947468225f,    -60.6153505185931f},
  { -168.876004352720f,    27.3733119168848f},
  { -117.819442211826f,    9.86516586603182f},
  { 168.876004339933f,    -27.3733119134699f},
  { 117.819442199355f,    -9.86516586429413f},
  { 11.1239956478932f,    27.3733119130858f},
  { 62.1805577877021f,    9.86516586259459f},
  { -11.1239956613407f,    -27.3733119165322f},
  { -110.436905267536f,    60.6153505204452f},
  { 69.5630947277636f,    60.6153505173552f},
  { -125.929940749245f,    -47.3994855979503f},
  { -126.671481040740f,    -23.4027352002794f},
  { 54.0700592527834f,    -47.3994856016111f},
  { -151.648882073130f,    -33.2364603810367f},
  { -53.3285189719047f,    23.4027352017874f},
  { 151.648882058869f,    33.2364603842090f},
  { 53.3285189601170f,    -23.4027352039908f},
  { 28.3511179269492f,    -33.2364603851095f},
  { 126.671481026299f,    23.4027352024511f},
  { -28.3511179389262f,    33.2364603819160f},
  { 125.929940732929f,    47.3994856000570f},
  { -54.0700592627114f,    47.3994855994707f},
  { 61.4093869712020f,    37.5359641921079f},
  { 41.1867022349720f,    22.3011497399151f},
  { -118.590613027003f,    37.5359641955588f},
  { 31.9165501791293f,    44.1290873505536f},
  { 138.813297752503f,    -22.3011497411599f},
  { -31.9165501940578f,    -44.1290873535754f},
  { -138.813297764599f,    22.3011497439225f},
  { -148.083449820620f,    44.1290873545683f},
  { -41.1867022490880f,    -22.3011497426817f},
  { 148.083449809271f,    -44.1290873515606f},
  { -61.4093869868180f,    -37.5359641938559f},
  { 118.590613016358f,    -37.5359641937859f},
  { 132.923697873404f,    4.73307797901005f},
  { 6.45099119915111f,    -42.7422526473549f},
  { -47.0763021263360f,    4.73307797785435f},
  { -83.0682214348878f,    46.8666308746944f},
  { 173.549008786020f,    42.7422526471375f},
  { 83.0682214256211f,    -46.8666308750510f},
  { -173.549008799468f,    -42.7422526436592f},
  { 96.9317785610360f,    46.8666308731931f},
  { -6.45099121192998f,    42.7422526438352f},
  { -96.9317785780300f,    -46.8666308727651f},
  { -132.923697886652f,    -4.73307797647834f},
  { 47.0763021134026f,    -4.73307798038859f}};
 
/* Minimum T-design of degree 13 (94 points) */
const float __Tdesign_degree_13_dirs_deg[94][2] =
{ { -40.3627167222348f,    68.6994138693883f},
  { 61.1178757094869f,    65.6841788540926f},
  { 141.729207778738f,    70.7473887065821f},
  { -131.254071010305f,    72.3178990997495f},
  { -154.879003534434f,    -12.6182154153575f},
  { -66.1952941496760f,    -9.78390290250878f},
  { 26.3619203195797f,    -11.9654063218404f},
  { 114.952572653282f,    -12.5785685168723f},
  { 37.0184004816904f,    51.1256389892300f},
  { 129.769829567165f,    51.9548524146586f},
  { -140.632268790346f,    50.1516259787950f},
  { -56.5007238296603f,    47.8775543682241f},
  { -65.0474273466871f,    12.5785685169632f},
  { 25.1209964655500f,    12.6182154151376f},
  { 113.804705850467f,    9.78390290268633f},
  { -153.638079680491f,    11.9654063218214f},
  { -134.514914083258f,    -9.72778866158662f},
  { -46.2302615549395f,    -8.36621679129740f},
  { 47.9052586063038f,    -9.73252662507003f},
  { 141.506162727637f,    -8.72815719945242f},
  { -17.8362968684834f,    -44.0982842994686f},
  { 69.3686740106101f,    -43.2665797312820f},
  { 151.216430500609f,    -42.6650502889612f},
  { -106.776151619671f,    -40.1759720348795f},
  { -50.2301704328105f,    -51.9548524144938f},
  { 39.3677312097665f,    -50.1516259788305f},
  { 123.499276170276f,    -47.8775543681000f},
  { -142.981599518156f,    -51.1256389893727f},
  { -179.192692804150f,    -60.7498597598460f},
  { -84.5683722244082f,    -54.0721250135385f},
  { 5.39023497898549f,    -58.0518216444931f},
  { 89.5021760546650f,    -60.7465965609431f},
  { -145.976954290766f,    31.0152557263501f},
  { -54.3906597983015f,    26.4284741481704f},
  { 28.9208513184387f,    32.5135882095920f},
  { 125.336198321601f,    30.9431238792627f},
  { 168.711773251522f,    -7.05940715762768f},
  { -112.485952534025f,    -10.3751837493173f},
  { -21.9560854554006f,    -9.60167976599116f},
  { 73.1112518340806f,    -8.31254840811588f},
  { 95.6758711125988f,    0.0405182785108394f},
  { -170.708278926686f,    2.32277503975178f},
  { -84.3241288875143f,    -0.0405182784656330f},
  { 9.29172107320429f,    -2.32277503993912f},
  { 9.18585986004928f,    -34.3279751514861f},
  { 98.2142505588550f,    -37.3058168381220f},
  { -179.203725583107f,    -40.4848300096384f},
  { -77.8092661173471f,    -31.6042234205206f},
  { -177.084812005157f,    -21.7372544942682f},
  { -93.7724854158139f,    -18.8290843901069f},
  { -2.71509126119301f,    -19.7973423473147f},
  { 90.5055865842376f,    -20.9130131157502f},
  { -106.888748165935f,    8.31254840848543f},
  { -11.2882267487850f,    7.05940715728591f},
  { 67.5140474661053f,    10.3751837496826f},
  { 158.043914544759f,    9.60167976557666f},
  { -118.882124290049f,    -65.6841788541697f},
  { -38.2707922214634f,    -70.7473887063923f},
  { 48.7459289902140f,    -72.3178990998148f},
  { 139.637283277007f,    -68.6994138693407f},
  { -54.6638016787848f,    -30.9431238791174f},
  { 34.0230457094863f,    -31.0152557263048f},
  { 125.609340201678f,    -26.4284741480840f},
  { -151.079148681228f,    -32.5135882098331f},
  { -170.814140140253f,    34.3279751514361f},
  { -81.7857494411369f,    37.3058168382986f},
  { 0.796274416838389f,    40.4848300092311f},
  { 102.190733882995f,    31.6042234207107f},
  { -28.7835694993777f,    42.6650502888879f},
  { 73.2238483805505f,    40.1759720348183f},
  { 162.163703131160f,    44.0982842994090f},
  { -110.631325989256f,    43.2665797315176f},
  { -89.4944134156443f,    20.9130131158586f},
  { 2.91518799464472f,    21.7372544938146f},
  { 86.2275145844840f,    18.8290843902342f},
  { 177.284908738826f,    19.7973423471420f},
  { 133.769738445099f,    8.36621679123653f},
  { -132.094741393724f,    9.73252662529703f},
  { -38.4938372724335f,    8.72815719936124f},
  { 45.4850859168882f,    9.72778866179206f},
  { -25.6021660105829f,    24.0412140934934f},
  { 55.1230998001090f,    30.2272431389321f},
  { 149.298950110694f,    28.0455421626317f},
  { -118.706558467820f,    26.0579506724807f},
  { 0.807307195922662f,    60.7498597594458f},
  { 95.4316277754395f,    54.0721250137300f},
  { -174.609765021233f,    58.0518216443168f},
  { -90.4978239451188f,    60.7465965612768f},
  { -124.876900199724f,    -30.2272431386341f},
  { -30.7010498895602f,    -28.0455421629911f},
  { 61.2934415322725f,    -26.0579506721723f},
  { 154.397833989464f,    -24.0412140935974f},
  { -132.915308725410f,    -85.6000936509801f},
  { 47.0846912731536f,    85.6000936508629f}};
 
/* Minimum T-design of degree 14 (108 points) */
const float __Tdesign_degree_14_dirs_deg[108][2] =
{ { -129.185496888476f,    8.10563028578741f},
  { 169.578599576646f,    -38.7292166126126f},
  { 50.8148695271600f,    8.12050690100986f},
  { -77.2740193615098f,    -50.1149231885907f},
  { 10.4239654092118f,    38.7310086728624f},
  { 77.2976960009371f,    50.1174305751531f},
  { -10.4119358669821f,    -38.7198037761506f},
  { 102.710075564305f,    -50.1077672707642f},
  { -169.569875076608f,    38.7180119969233f},
  { -102.712992621563f,    50.1052603901109f},
  { 129.194616327794f,    -8.11282927824916f},
  { -50.8032326138493f,    -8.11330777101311f},
  { -4.59215033966074f,    -56.0145426200334f},
  { -93.0961080949996f,    33.8503331657228f},
  { 175.391842883684f,    -56.0251031820136f},
  { 146.110504990858f,    -2.57401246703588f},
  { -86.8931538003163f,    -33.8602245481812f},
  { -146.100412500120f,    2.56455577491969f},
  { 86.9111644059348f,    33.8608402235944f},
  { -33.8888402494298f,    -2.57007990733392f},
  { 93.0988554959334f,    -33.8509487698007f},
  { 33.8995035311197f,    2.57953664040591f},
  { 4.60388295935663f,    56.0258986613491f},
  { -175.382824609272f,    56.0137473745907f},
  { 106.566908554445f,    26.0969762431768f},
  { 27.0704791250355f,    -14.8221953013083f},
  { -73.4398224140619f,    26.0907279761036f},
  { -30.2019611726677f,    59.4125144873598f},
  { 152.942234123029f,    14.8267023571315f},
  { 30.2026449688438f,    -59.4026682881680f},
  { -152.930483939354f,    -14.8368475821330f},
  { 149.822214569457f,    59.4076496872466f},
  { -27.0614738204129f,    14.8323403149657f},
  { -149.802145490903f,    -59.4174973348394f},
  { -106.551181547953f,    -26.1002232021554f},
  { 73.4448527743907f,    -26.0874812806078f},
  { -171.424549759738f,    77.4508785133046f},
  { 91.8987958716823f,    -12.3962958134667f},
  { 8.53903505084858f,    77.4636176315132f},
  { -12.4022480507938f,    -1.84616868079121f},
  { 88.1115107175677f,    12.4061962956428f},
  { 12.4127047713575f,    1.85729530242821f},
  { -88.0986284057768f,    -12.4058195758491f},
  { 167.597360255578f,    -1.85516686202351f},
  { -91.8909209594892f,    12.3959191080322f},
  { -167.587061725650f,    1.84404025367733f},
  { 171.427293256838f,    -77.4621438946096f},
  { -8.52106137787343f,    -77.4523509482603f},
  { -122.725444898284f,    -10.4436681618452f},
  { -167.646619541773f,    -32.1304560946658f},
  { 57.2737763995243f,    -10.4291751560142f},
  { -108.800959121800f,    -55.8290478813134f},
  { -12.3490789438205f,    32.1283371856927f},
  { 108.827221090328f,    55.8253737505810f},
  { 12.3579262049535f,    -32.1172082630069f},
  { 71.1878632374232f,    -55.8159974423682f},
  { 167.658526826702f,    32.1193269135384f},
  { -71.1933648961921f,    55.8196706876724f},
  { 122.737588435530f,    10.4375080894726f},
  { -57.2651633537552f,    10.4353350634210f},
  { -135.835854784211f,    -23.0547585640994f},
  { -148.583253700629f,    -41.3187537286755f},
  { 44.1637920456130f,    -23.0396843683594f},
  { -120.662099788593f,    -39.8769052826722f},
  { -31.4137988125835f,    41.3135904099716f},
  { 120.680663009779f,    39.8710937105608f},
  { 31.4189576996095f,    -41.3038678530177f},
  { 59.3339359050566f,    -39.8625737566942f},
  { 148.598849815269f,    41.3090304016975f},
  { -59.3317418485565f,    39.8683846070324f},
  { 135.849609497709f,    23.0465850901611f},
  { -44.1567906522068f,    23.0478574234931f},
  { -161.547774160409f,    20.6214832030571f},
  { 130.038592068425f,    -62.5981252668102f},
  { 18.4500454157052f,    20.6354249039959f},
  { -68.3479254388390f,    -17.2274007359150f},
  { 49.9594914575609f,    62.6057092231770f},
  { 68.3615869487824f,    17.2316030343816f},
  { -49.9322890507680f,    -62.5983778933698f},
  { 111.647658776834f,    -17.2223955106639f},
  { -130.045036899004f,    62.5907958085244f},
  { -111.640563285857f,    17.2181934215587f},
  { 161.556794742584f,    -20.6322904708357f},
  { -18.4383108625927f,    -20.6246174136712f},
  { -105.229923721163f,    -3.38418721629137f},
  { -176.495407017449f,    -15.2142387436252f},
  { 74.7695811147565f,    -3.37163564281617f},
  { -102.637896944791f,    -74.4094065275369f},
  { -3.49690334883675f,    15.2136338742552f},
  { 102.688108006896f,    74.4069090611730f},
  { 3.50709175282307f,    -15.2022624413437f},
  { 77.3300588827299f,    -74.3972447248446f},
  { 176.505973637731f,    15.2028672780281f},
  { -77.3594900583547f,    74.3997406824127f},
  { 105.240951032319f,    3.38119337243154f},
  { -74.7598514248982f,    3.37462945722995f},
  { -142.390512576284f,    25.4175908027638f},
  { 142.077529927039f,    -45.6868543254021f},
  { 37.6090614633499f,    25.4326612225385f},
  { -59.0248292186823f,    -33.4439538525117f},
  { 37.9248440888004f,    45.6929425950841f},
  { 59.0416596504450f,    33.4498158632456f},
  { -37.9072953200755f,    -45.6839547544076f},
  { 120.965352734802f,    -33.4413214611586f},
  { -142.074323295910f,    45.6778674627608f},
  { -120.961426152688f,    33.4354600243172f},
  { 142.397585749735f,    -25.4266164045797f},
  { -37.5953788557179f,    -25.4236351680798f}};
 
/* Minimum T-design of degree 15 (120 points) */
const float __Tdesign_degree_15_dirs_deg[120][2] =
{ { -30.6030525550461f,    6.94295470706933f},
  { 166.556601881679f,    58.6896167148965f},
  { 149.397921574412f,    6.95676040033414f},
  { 81.9503184046850f,    -30.3562374013217f},
  { 13.4838352132044f,    -58.6862798372820f},
  { -81.9279696395992f,    30.3552068726552f},
  { -13.4632635060741f,    58.6787728253845f},
  { -98.0553212926679f,    -30.3693638204857f},
  { -166.541916444220f,    -58.6821134278307f},
  { 98.0687585715236f,    30.3704560408842f},
  { 30.6215511098796f,    -6.94955577140730f},
  { -149.380390687206f,    -6.95008925738623f},
  { 106.689953124681f,    -22.6783689069045f},
  { -23.5657187755504f,    -15.3628427250753f},
  { -73.3114441250527f,    -22.6942854521603f},
  { -145.501414237039f,    62.1042310518677f},
  { -156.412773408714f,    15.3570707316218f},
  { 145.527116313848f,    -62.0978793943380f},
  { 156.431582868341f,    -15.3501087206496f},
  { 34.4680326551376f,    62.1059340346835f},
  { 23.5828302580784f,    15.3556650727373f},
  { -34.4587547006376f,    -62.1123240120557f},
  { -106.668780509784f,    22.6806221234814f},
  { 73.3264081825364f,    22.6921040187581f},
  { 166.815146476476f,    1.39137137645932f},
  { 6.09164877259154f,    -76.7377960648265f},
  { -13.1851422017595f,    1.38060121346851f},
  { -88.5665379871222f,    13.1827681324909f},
  { 173.986274618312f,    76.7393112171196f},
  { 88.5863712660644f,    -13.1829911005176f},
  { -173.972192649359f,    -76.7316416441619f},
  { 91.4317067978856f,    13.1972659475335f},
  { -6.07044089187156f,    76.7301145219168f},
  { -91.4155231870143f,    -13.1971051505712f},
  { -166.797273031735f,    -1.38387705718332f},
  { 13.2031163001391f,    -1.38813486593518f},
  { -74.6719653628180f,    48.1128159205733f},
  { 130.860845670697f,    10.1648476117330f},
  { 105.324001632841f,    48.1286252881803f},
  { 13.3402738550233f,    -40.0816483636324f},
  { 49.1587806791108f,    -10.1540507848293f},
  { -13.3209329958570f,    40.0741920019256f},
  { -49.1397371265836f,    10.1490822313170f},
  { -166.672794690516f,    -40.0774058487576f},
  { -130.843884042363f,    -10.1597669438345f},
  { 166.689200908705f,    40.0849666149935f},
  { 74.6979186340827f,    -48.1147886327798f},
  { -105.314588513838f,    -48.1265844469817f},
  { -126.994710754480f,    26.5534844401442f},
  { 147.963786150663f,    -32.5685324439693f},
  { 52.9979184448058f,    26.5602526628589f},
  { -50.2839814792401f,    -45.5940649038881f},
  { 32.0464832809211f,    32.5759524833013f},
  { 50.2955756473413f,    45.5891069117364f},
  { -32.0312406436033f,    -32.5825905716800f},
  { 129.712795354186f,    -45.5781144439024f},
  { -147.943226072877f,    32.5749436398314f},
  { -129.689094831424f,    45.5830214583665f},
  { 127.015829484310f,    -26.5488550940039f},
  { -52.9830053081905f,    -26.5648704461645f},
  { -171.925165097520f,    30.3656373764858f},
  { 103.474315132854f,    -58.6762932898078f},
  { 8.06598910342026f,    30.3599497256541f},
  { -59.3793154805561f,    -6.95793281328386f},
  { 76.5377173373163f,    58.6902848585247f},
  { 59.3965972400983f,    6.95406151527783f},
  { -76.5325167840642f,    -58.6920609528879f},
  { 120.620572530444f,    -6.94173212922671f},
  { -103.444514431496f,    58.6781755803937f},
  { -120.601682190330f,    6.94569013736595f},
  { 171.943791968762f,    -30.3580618441019f},
  { -8.04868833080616f,    -30.3676509880131f},
  { 40.8591506674273f,    10.1586784460910f},
  { 15.3172714874563f,    48.1188014520829f},
  { -139.138012788032f,    10.1552322152725f},
  { 76.6795691484389f,    40.0856595700319f},
  { 164.685199993217f,    -48.1151686422521f},
  { -76.6680975158839f,    -40.0873731256771f},
  { -164.665133980975f,    48.1225223368022f},
  { -103.311377388557f,    40.0735260689792f},
  { -15.3018010383944f,    -48.1263067557738f},
  { 103.335438313858f,    -40.0716468871635f},
  { -40.8419970065716f,    -10.1644693751345f},
  { 139.156972194678f,    -10.1493915261064f},
  { 103.203017496907f,    -1.37818298743888f},
  { -1.41295359216869f,    -13.1940817732791f},
  { -76.7970625008060f,    -1.39388969574653f},
  { -96.0226016809032f,    76.7280399662938f},
  { -178.565790556190f,    13.1937156944364f},
  { 96.0727952593646f,    -76.7271870367777f},
  { 178.583741131798f,    -13.1860167806370f},
  { 83.9384305400478f,    76.7414148352344f},
  { 1.43082080108730f,    13.1863482688284f},
  { -83.9533413278650f,    -76.7422528505934f},
  { -103.184809097502f,    1.37992019271170f},
  { 76.8149044656686f,    1.39206982161959f},
  { 37.0203773932360f,    -26.5556799548844f},
  { -39.6998537331091f,    45.5785590048425f},
  { -142.987611559503f,    -26.5580137886591f},
  { 122.051959505631f,    32.5835914894780f},
  { -140.293652413608f,    -45.5876530266288f},
  { -122.038265069292f,    -32.5795114954413f},
  { 140.306374919687f,    45.5935766807050f},
  { -57.9487870815201f,    32.5674048936121f},
  { 39.7225744490892f,    -45.5845144211182f},
  { 57.9707590481942f,    -32.5714872904771f},
  { -37.0001343655174f,    26.5495567479843f},
  { 143.003247815211f,    26.5642004349055f},
  { 163.331127304408f,    22.6920948057362f},
  { 55.5479236516533f,    -62.1013914093322f},
  { -16.6736304241223f,    22.6806589773217f},
  { -66.4147692500420f,    15.3482860362968f},
  { 124.485029630888f,    62.1131464175266f},
  { 66.4346475986745f,    -15.3513839575877f},
  { -124.479439274632f,    -62.1088084825996f},
  { 113.584840357941f,    15.3644980586459f},
  { -55.5182605036017f,    62.0970279081496f},
  { -113.568822266193f,    -15.3614254483317f},
  { -163.314069620612f,    -22.6846279659434f},
  { 16.6925187091527f,    -22.6879825807004f}};
 
/* Minimum T-design of degree 16 (144 points) */
const float __Tdesign_degree_16_dirs_deg[144][2] =
{ { -10.5692580668100f,    -17.3490128634352f},
  { -120.415474946769f,    69.7642225220975f},
  { 169.426697678052f,    -17.3466306179260f},
  { 107.629281568279f,    -10.0793856720614f},
  { -59.5674172539630f,    -69.7763953095265f},
  { -107.629493132161f,    10.0801907586439f},
  { 59.5651193014662f,    69.7750019669784f},
  { -72.3715136529922f,    -10.0909592824967f},
  { 120.418832045969f,    -69.7630732527928f},
  { 72.3705387467529f,    10.0908849630425f},
  { 10.5699823270029f,    17.3489915451677f},
  { -169.426851150349f,    17.3476277272366f},
  { -30.7728814706980f,    68.2546206344998f},
  { 101.529181734204f,    18.5653877408229f},
  { 149.250234431564f,    68.2619792676765f},
  { 18.9183978612362f,    -10.9197242075287f},
  { 78.4729799557400f,    -18.5558892226653f},
  { -18.9161109968480f,    10.9195275229078f},
  { -78.4723066816396f,    18.5565169424192f},
  { -161.085243560336f,    -10.9220975953767f},
  { -101.530063994217f,    -18.5648176173994f},
  { 161.085855454581f,    10.9237834974412f},
  { 30.7790837424989f,    -68.2562996173874f},
  { -149.255648697558f,    -68.2594892022576f},
  { 56.4638592172755f,    41.2645742763346f},
  { 46.4626904606488f,    24.5386896277818f},
  { -123.528839291756f,    41.2565889648213f},
  { 32.1932295461248f,    38.8027347956192f},
  { 133.534545076742f,    -24.5310453346374f},
  { -32.1935458377634f,    -38.8041545028931f},
  { -133.533477606995f,    24.5319420428588f},
  { -147.797881221742f,    38.7980990097138f},
  { -46.4626630742447f,    -24.5400749997299f},
  { 147.799544204027f,    -38.7965984357137f},
  { -56.4649576930965f,    -41.2658215291547f},
  { 123.530547454259f,    -41.2555316199835f},
  { 84.7385596473317f,    27.3132538556364f},
  { 27.4072860474693f,    4.67593317316088f},
  { -95.2612516264878f,    27.3036967398252f},
  { 10.0607591758466f,    62.2287426217158f},
  { 152.592710471291f,    -4.67007594116539f},
  { -10.0604693351594f,    -62.2317767049329f},
  { -152.592615409799f,    4.67188744845125f},
  { -169.918387889403f,    62.2272712110016f},
  { -27.4047652820400f,    -4.67684895484045f},
  { 169.918493477140f,    -62.2246416140826f},
  { -84.7390238025025f,    -27.3120311727342f},
  { 95.2622793653641f,    -27.3027426350066f},
  { 136.272846725200f,    -0.726139068263599f},
  { -1.05456977390436f,    -46.2698051615206f},
  { -43.7263256019408f,    -0.737666959763443f},
  { -91.0084089447853f,    43.7170295842697f},
  { -178.936314291048f,    46.2682278552731f},
  { 91.0100541861312f,    -43.7163112498585f},
  { 178.938490558618f,    -46.2666218304286f},
  { 88.9860902890987f,    43.7285680951606f},
  { 1.05095788619312f,    46.2682407577363f},
  { -88.9851906686018f,    -43.7278600822776f},
  { -136.273314433943f,    0.726484363994244f},
  { 43.7273191822901f,    0.733967099281741f},
  { 55.2321077221357f,    10.8187456245361f},
  { 13.0867814081219f,    34.0654299770448f},
  { -124.767898552651f,    10.8099467408727f},
  { 71.4751302534919f,    53.7984109774923f},
  { 166.905549455530f,    -34.0625862919868f},
  { -71.4765158530160f,    -53.8002805142714f},
  { -166.904587570338f,    34.0633858486074f},
  { -108.515564585463f,    53.7864186881779f},
  { -13.0869589355977f,    -34.0644403811701f},
  { 108.517274377512f,    -53.7853093207457f},
  { -55.2337689585088f,    -10.8200079671294f},
  { 124.767519417537f,    -10.8096092876561f},
  { -105.493359369733f,    -68.1345228940484f},
  { -111.151973933085f,    -5.71277564515985f},
  { 74.5244447329726f,    -68.1205741555505f},
  { -173.885132403874f,    -21.0401043953034f},
  { -68.8521018079939f,    5.70313885775370f},
  { 173.885050918764f,    21.0419786777516f},
  { 68.8513569996117f,    -5.70297394874866f},
  { 6.12041448982713f,    -21.0387333986971f},
  { 111.151515131908f,    5.71357243375474f},
  { -6.11913621739966f,    21.0397756114589f},
  { 105.487055344890f,    68.1331981897040f},
  { -74.5188619841755f,    68.1214716326340f},
  { 35.2822222163987f,    -15.1801841162885f},
  { -25.1732516880600f,    51.9826514887145f},
  { -144.722913967824f,    -15.1859965048827f},
  { 108.386507250934f,    33.8824333892584f},
  { -154.839566662519f,    -51.9856067440744f},
  { -108.385758587361f,    -33.8826426573830f},
  { 154.840828582605f,    51.9884126722963f},
  { -71.6110721306039f,    33.8714084774643f},
  { 25.1699762263473f,    -51.9843011897216f},
  { 71.6126173250777f,    -33.8705490198003f},
  { -35.2810594358470f,    15.1763090469469f},
  { 144.722474074749f,    15.1863112389402f},
  { -125.277803641269f,    -28.5561977838671f},
  { -146.317489805034f,    -30.4888082061806f},
  { 54.7220842889970f,    -28.5463137051834f},
  { -133.292600372594f,    -45.8199818171681f},
  { -33.6854220654234f,    30.4794807422719f},
  { 133.295169860873f,    45.8200619710773f},
  { 33.6830420572493f,    -30.4828689919959f},
  { 46.7098267598019f,    -45.8106991831118f},
  { 146.318736830907f,    30.4889588527258f},
  { -46.7107531920589f,    45.8077510168776f},
  { 125.278543193551f,    28.5567151663926f},
  { -54.7226679373581f,    28.5424675755949f},
  { -144.402199049652f,    54.7141577397485f},
  { 112.382216591782f,    -28.0100385212576f},
  { 35.5834085793474f,    54.7193853715013f},
  { -29.9155874729000f,    -19.6471282266303f},
  { 67.6163420587218f,    28.0211878299760f},
  { 29.9151078604395f,    19.6461577548916f},
  { -67.6164804090156f,    -28.0221553885221f},
  { 150.081679085309f,    -19.6396879622134f},
  { -112.381365317985f,    28.0105570315277f},
  { -150.081127534239f,    19.6412999777121f},
  { 144.402936805264f,    -54.7127597303097f},
  { -35.5837994140428f,    -54.7203576209200f},
  { 68.5348504928164f,    -52.8527273534571f},
  { -54.8218918027732f,    12.7570858971645f},
  { -111.464947340552f,    -52.8652964226689f},
  { 164.510735700738f,    34.1892226850382f},
  { -125.181243085238f,    -12.7710900404128f},
  { -164.510172672569f,    -34.1865270720665f},
  { 125.180742749445f,    12.7714932994183f},
  { -15.4967238792034f,    34.1855682977571f},
  { 54.8232484475423f,    -12.7607435822084f},
  { 15.4931170933516f,    -34.1868032875460f},
  { -68.5328366887261f,    52.8538785361128f},
  { 111.467075873460f,    52.8645433650926f},
  { 91.4783759173555f,    -7.37343377883849f},
  { -7.38018069449028f,    -1.46605904801040f},
  { -88.5233821655574f,    -7.38351008527854f},
  { -168.689339775081f,    82.4742907515114f},
  { -172.618562111102f,    1.46559142196641f},
  { 168.689017629111f,    -82.4717071901232f},
  { 172.618489604721f,    -1.46441483340862f},
  { 11.2157017776617f,    82.4763593030642f},
  { 7.38236788128392f,    1.46620895892741f},
  { -11.2117036062431f,    -82.4789181367532f},
  { -91.4785749918475f,    7.37448337501027f},
  { 88.5224297767631f,    7.38438652912129f}};
 
/* Minimum T-design of degree 17 (156 points) */
const float __Tdesign_degree_17_dirs_deg[156][2] =
{ { -110.972536098452f,    -81.3395149878408f},
  { -98.0945259291915f,    -3.08934606926242f},
  { 69.0283101966918f,    -81.3395963121933f},
  { -176.879500974752f,    -8.08271861041067f},
  { -81.9053305069526f,    3.08941705867335f},
  { 176.879644538453f,    8.08278710024119f},
  { 81.9054851307679f,    -3.08940328913739f},
  { 3.12051971992014f,    -8.08274990022289f},
  { 98.0946906822435f,    3.08939807146030f},
  { -3.12033418366235f,    8.08275384646156f},
  { 110.971757607529f,    81.3396073060199f},
  { -69.0272255211550f,    81.3394832453476f},
  { 145.758325050956f,    30.5199949962486f},
  { 46.3338654430728f,    -45.4090808372840f},
  { -34.2417244572974f,    30.5199299435608f},
  { -54.5065763702847f,    28.9944543220334f},
  { 133.666175283428f,    45.4090645714201f},
  { 54.5065169257390f,    -28.9946358709077f},
  { -133.666075964290f,    -45.4090639295985f},
  { 125.493507490318f,    28.9945948799985f},
  { -46.3338672664529f,    45.4089150225299f},
  { -125.493394782705f,    -28.9945644971856f},
  { -145.758189836803f,    -30.5199956551973f},
  { 34.2417015167707f,    -30.5199717945651f},
  { 159.575321832626f,    41.3951427412058f},
  { 68.4011541800515f,    -44.6686954718411f},
  { -20.4246846261942f,    41.3950488549860f},
  { -46.7530721727418f,    15.1762870269464f},
  { 111.598907199965f,    44.6686624702884f},
  { 46.7532214376113f,    -15.1763613881014f},
  { -111.598821312324f,    -44.6685911089863f},
  { 133.246909041379f,    15.1763548809948f},
  { -68.4011026670182f,    44.6685187574964f},
  { -133.246756962063f,    -15.1763306571922f},
  { -159.575235433158f,    -41.3951042577738f},
  { 20.4247512806759f,    -41.3951386279467f},
  { 85.4331069665815f,    -37.9336689610989f},
  { -38.0219422832657f,    3.60044246504075f},
  { -94.5668221766801f,    -37.9336369935624f},
  { 174.167181422254f,    51.8336299061990f},
  { -141.977923622517f,    -3.60052335289898f},
  { -174.167161198305f,    -51.8335093466070f},
  { 141.978017527634f,    3.60052739735483f},
  { -5.83282102213420f,    51.8335060526221f},
  { 38.0221451086255f,    -3.60052175089752f},
  { 5.83286258546759f,    -51.8336195514750f},
  { -85.4331017546707f,    37.9336600665386f},
  { 94.5669635429985f,    37.9336717569877f},
  { 21.1823835996204f,    27.1703161950420f},
  { 54.8552196599246f,    56.0519373127499f},
  { -158.817667169175f,    27.1703764189990f},
  { 61.1687858728062f,    18.7515034281209f},
  { 125.144826414049f,    -56.0519088097055f},
  { -61.1686424166986f,    -18.7515067531668f},
  { -125.144783207922f,    56.0520170026195f},
  { -118.831333169078f,    18.7515075100248f},
  { -54.8552325260821f,    -56.0520018474777f},
  { 118.831357033983f,    -18.7514876111844f},
  { -21.1821737960870f,    -27.1703273487209f},
  { 158.817752395942f,    -27.1702501653088f},
  { 104.655973590479f,    -9.56052038782342f},
  { -9.87572204741232f,    -14.4479351672395f},
  { -75.3439962252486f,    -9.56049660768317f},
  { -123.650852748573f,    72.5589038610187f},
  { -170.124133559486f,    14.4479810651928f},
  { 123.651377037836f,    -72.5587964003922f},
  { 170.124261965706f,    -14.4478957329142f},
  { 56.3486516053099f,    72.5588326417427f},
  { 9.87590710801076f,    14.4479358622388f},
  { -56.3489612874038f,    -72.5588747160005f},
  { -104.655934361393f,    9.56053438641502f},
  { 75.3441507750264f,    9.56049031651235f},
  { 25.9352433504815f,    -16.8263454567228f},
  { -34.6629602764395f,    59.4049520144158f},
  { -154.064725964219f,    -16.8263938405563f},
  { 108.587307515400f,    24.7481093505154f},
  { -145.337042726548f,    -59.4050775637726f},
  { -108.587166936804f,    -24.7480813625633f},
  { 145.337024797510f,    59.4051213680066f},
  { -71.4127913520217f,    24.7480131711128f},
  { 34.6630103111907f,    -59.4051325021881f},
  { 71.4127455463276f,    -24.7481551074827f},
  { -25.9351333497229f,    16.8263470460926f},
  { 154.064872752799f,    16.8263949148262f},
  { -100.890653808628f,    26.4867629664574f},
  { 153.095389375993f,    -9.73572407837462f},
  { 79.1094689486786f,    26.4867038147623f},
  { -20.7650174418830f,    -61.5121429737782f},
  { 26.9048023491372f,    9.73577822208466f},
  { 20.7650094793833f,    61.5120919702165f},
  { -26.9045763350532f,    -9.73578359740380f},
  { 159.234989909912f,    -61.5120095244715f},
  { -153.095320693647f,    9.73577672831727f},
  { -159.234918273987f,    61.5121876738641f},
  { 100.890617375289f,    -26.4866867526547f},
  { -79.1093472045108f,    -26.4866920777842f},
  { 44.3136042236380f,    12.2784148864384f},
  { 17.3042148418974f,    44.3597818131229f},
  { -135.686522732100f,    12.2784100472036f},
  { 73.0820593381593f,    43.0474367769055f},
  { 162.695847122876f,    -44.3597017539863f},
  { -73.0819188464220f,    -43.0474262674942f},
  { -162.695765371418f,    44.3598645801098f},
  { -106.917995967658f,    43.0475197742591f},
  { -17.3041690092237f,    -44.3598140007833f},
  { 106.918015628643f,    -43.0474025708186f},
  { -44.3133852955836f,    -12.2785203404408f},
  { 135.686584721680f,    -12.2784215377938f},
  { -169.079669371546f,    -24.5321909536177f},
  { -112.542166671839f,    -63.2850601072096f},
  { 10.9202953872870f,    -24.5321908793467f},
  { -114.929999529610f,    -9.92395631971344f},
  { -67.4576447966383f,    63.2849658247549f},
  { 114.930166180530f,    9.92397510754817f},
  { 67.4579214268390f,    -63.2851359676343f},
  { 65.0699795536169f,    -9.92401372287082f},
  { 112.542146133756f,    63.2851183198918f},
  { -65.0698516207557f,    9.92390739777342f},
  { 169.079802219111f,    24.5322412571671f},
  { -10.9202113755098f,    24.5321946491817f},
  { 93.2040875742355f,    -57.3930220085365f},
  { -57.4335812294807f,    -1.72597809895388f},
  { -86.7960241525694f,    -57.3929860941125f},
  { -177.952273324117f,    32.5497631173123f},
  { -122.566253987475f,    1.72593957294755f},
  { 177.952374311331f,    -32.5496484135080f},
  { 122.566350583694f,    -1.72594309051837f},
  { 2.04775449117076f,    32.5496635362235f},
  { 57.4338233352979f,    1.72591921625950f},
  { -2.04759683730983f,    -32.5497546915263f},
  { -93.2038717181709f,    57.3930478036049f},
  { 86.7959914092532f,    57.3930448748746f},
  { -17.5897066057983f,    3.03732751711178f},
  { 170.041283651154f,    72.1581357589733f},
  { 162.410264047604f,    3.03735885797477f},
  { 86.8139300357902f,    -17.5643027243221f},
  { 9.95871784192333f,    -72.1581260767696f},
  { -86.8139808546443f,    17.5643089786731f},
  { -9.95884326138181f,    72.1579520781074f},
  { -93.1860064822312f,    -17.5642466145111f},
  { -170.041415817683f,    -72.1579882194655f},
  { 93.1861408789812f,    17.5642898521383f},
  { 17.5899070081613f,    -3.03728636624082f},
  { -162.410130590415f,    -3.03733315883086f},
  { 39.3792257392670f,    44.2573534137099f},
  { 56.9313776923427f,    33.6148193811549f},
  { -140.620759157715f,    44.2573759844125f},
  { 38.4239055017828f,    27.0264132991360f},
  { 123.068707795201f,    -33.6147936065186f},
  { -38.4237030347613f,    -27.0264785477125f},
  { -123.068677102487f,    33.6148394522083f},
  { -141.576163554034f,    27.0264135594767f},
  { -56.9312444104479f,    -33.6148138613919f},
  { 141.576226557237f,    -27.0264010423640f},
  { -39.3791791176139f,    -44.2574050937807f},
  { 140.620835015981f,    -44.2573180792070f}};
 
/* Minimum T-design of degree 18 (180 points) */
const float __Tdesign_degree_18_dirs_deg[180][2] =
{ { 165.522525351678f,    26.5185969118445f},
  { 63.3884960659874f,    -60.0402391549481f},
  { -14.4774747587378f,    26.5185969244391f},
  { -62.7356215863733f,    12.9262574799323f},
  { 116.611503753114f,    60.0402392311778f},
  { 62.7356216534755f,    -12.9262573768089f},
  { -116.611503960788f,    -60.0402392777927f},
  { 117.264378479103f,    12.9262574013180f},
  { -63.3884961827724f,    60.0402393764858f},
  { -117.264378506232f,    -12.9262575163645f},
  { -165.522525403520f,    -26.5185967690928f},
  { 14.4774746957471f,    -26.5185968169478f},
  { -150.217450616133f,    -21.6221948527669f},
  { -141.410000251229f,    -53.7887936217025f},
  { 29.7825495902173f,    -21.6221950203635f},
  { -114.546102790075f,    -27.5006115805657f},
  { -38.5899997172093f,    53.7887938971789f},
  { 114.546102736916f,    27.5006114363632f},
  { 38.5899997865273f,    -53.7887936503052f},
  { 65.4538974225092f,    -27.5006114292486f},
  { 141.410000115890f,    53.7887937976550f},
  { -65.4538971677670f,    27.5006116108567f},
  { 150.217450576809f,    21.6221950037115f},
  { -29.7825495511979f,    21.6221950095317f},
  { -163.468939687510f,    81.9141711880659f},
  { 92.3148380088438f,    -7.74950785743483f},
  { 16.5310604080828f,    81.9141711765953f},
  { -7.75575993532564f,    -2.29368526450881f},
  { 87.6851620086179f,    7.74950781982179f},
  { 7.75575978589441f,    2.29368524973419f},
  { -87.6851621029077f,    -7.74950792835357f},
  { 172.244240168478f,    -2.29368534133714f},
  { -92.3148378847329f,    7.74950778602442f},
  { -172.244240142217f,    2.29368535781371f},
  { 163.468940319517f,    -81.9141712591068f},
  { -16.5310594957412f,    -81.9141711307485f},
  { -79.9069240872412f,    -73.4928298922544f},
  { -106.265313752353f,    2.85417063577255f},
  { 100.093075450962f,    -73.4928298832334f},
  { 177.027037325915f,    -16.2445778332985f},
  { -73.7346862724408f,    -2.85417076248328f},
  { -177.027037359582f,    16.2445778708826f},
  { 73.7346861330546f,    2.85417077799392f},
  { -2.97296266678957f,    -16.2445777170525f},
  { 106.265313900319f,    -2.85417075916001f},
  { 2.97296252214977f,    16.2445777463947f},
  { 79.9069242475240f,    73.4928297213284f},
  { -100.093075924320f,    73.4928297504114f},
  { -43.1928640166220f,    73.6304207741543f},
  { 101.367856910908f,    11.8570587394614f},
  { 136.807135671159f,    73.6304207358966f},
  { 12.0874142750063f,    -11.1221753611675f},
  { 78.6321431755501f,    -11.8570587892693f},
  { -12.0874143568441f,    11.1221753851378f},
  { -78.6321430525525f,    11.8570588882244f},
  { -167.912585805617f,    -11.1221752564724f},
  { -101.367856964503f,    -11.8570589676836f},
  { 167.912585849640f,    11.1221753505886f},
  { 43.1928639454143f,    -73.6304205435030f},
  { -136.807135980905f,    -73.6304206111304f},
  { 109.863477411331f,    -34.8309444444304f},
  { -36.4953684573441f,    -16.1948859619229f},
  { -70.1365225856530f,    -34.8309444309736f},
  { -153.972978190969f,    50.5342660057627f},
  { -143.504631539358f,    16.1948859540727f},
  { 153.972978187359f,    -50.5342660958429f},
  { 143.504631621503f,    -16.1948859557381f},
  { 26.0270217639140f,    50.5342659511289f},
  { 36.4953682958062f,    16.1948859321165f},
  { -26.0270217764730f,    -50.5342659584325f},
  { -109.863477345633f,    34.8309442863438f},
  { 70.1365226011247f,    34.8309443621136f},
  { -23.3144176246880f,    -6.54377493040509f},
  { -163.836601816190f,    65.8340912397072f},
  { 156.685582511874f,    -6.54377498490282f},
  { 97.1198721371224f,    -23.1536444499380f},
  { -16.1633979077694f,    -65.8340911421026f},
  { -97.1198719381115f,    23.1536443807155f},
  { 16.1633982812712f,    65.8340911823371f},
  { -82.8801280056832f,    -23.1536445259357f},
  { 163.836602088907f,    -65.8340912805086f},
  { 82.8801279292869f,    23.1536443812616f},
  { 23.3144174717292f,    6.54377488581314f},
  { -156.685582444247f,    6.54377505059661f},
  { -0.871525155053854f,    -31.9228878345329f},
  { -91.3985860869862f,    58.0664743343015f},
  { 179.128474793439f,    -31.9228879881299f},
  { 121.925863139225f,    -0.739708138349097f},
  { -88.6014139907392f,    -58.0664745214493f},
  { -121.925862927300f,    0.739708140763914f},
  { 88.6014140770374f,    58.0664742415090f},
  { -58.0741371324967f,    -0.739708171109085f},
  { 91.3985859230815f,    -58.0664744459172f},
  { 58.0741369468673f,    0.739708221512544f},
  { 0.871525106485463f,    31.9228879048823f},
  { -179.128474897751f,    31.9228880865407f},
  { 163.118919203476f,    43.3490042807202f},
  { 72.9009079952637f,    -44.0950803474695f},
  { -16.8810807237829f,    43.3490042469511f},
  { -45.3900610991516f,    12.1906201180173f},
  { 107.099092058332f,    44.0950802946323f},
  { 45.3900611170782f,    -12.1906201460423f},
  { -107.099092029623f,    -44.0950804951930f},
  { 134.609939068526f,    12.1906201756408f},
  { -72.9009079168893f,    44.0950804987426f},
  { -134.609939017185f,    -12.1906201217856f},
  { -163.118919307274f,    -43.3490040821782f},
  { 16.8810806660299f,    -43.3490041124859f},
  { -114.226485782122f,    50.3719680420707f},
  { 127.058874767029f,    -15.1720365932007f},
  { 65.7735143230453f,    50.3719681032687f},
  { -18.7680122129425f,    -35.5652767976860f},
  { 52.9411252032868f,    15.1720366801078f},
  { 18.7680121845148f,    35.5652767553954f},
  { -52.9411253805515f,    -15.1720366270455f},
  { 161.231987695175f,    -35.5652769283117f},
  { -127.058874580761f,    15.1720366187415f},
  { -161.231987809323f,    35.5652769144754f},
  { 114.226485786593f,    -50.3719682654292f},
  { -65.7735141972913f,    -50.3719682192744f},
  { 54.1696638774737f,    30.1608310237706f},
  { 35.6306478157225f,    30.4068206160989f},
  { -125.830335996810f,    30.1608309118647f},
  { 45.2106162344126f,    44.5067175274920f},
  { 144.369352021074f,    -30.4068206860435f},
  { -45.2106162718128f,    -44.5067174987149f},
  { -144.369352124760f,    30.4068205977378f},
  { -134.789383740334f,    44.5067174067404f},
  { -35.6306478988259f,    -30.4068206396040f},
  { 134.789383697533f,    -44.5067175741724f},
  { -54.1696639660126f,    -30.1608309659934f},
  { 125.830336002098f,    -30.1608309772511f},
  { 126.198365586012f,    41.7296556110488f},
  { 47.8615829548800f,    -26.1516257329903f},
  { -53.8016343365832f,    41.7296557416691f},
  { -33.5111352365998f,    37.0306401796118f},
  { 132.138417183687f,    26.1516257455572f},
  { 33.5111352223607f,    -37.0306400834847f},
  { -132.138417282523f,    -26.1516257480742f},
  { 146.488864794235f,    37.0306401121596f},
  { -47.8615827989520f,    26.1516257755240f},
  { -146.488864880324f,    -37.0306399818889f},
  { -126.198365627788f,    -41.7296556060802f},
  { 53.8016344598902f,    -41.7296555261562f},
  { -161.752580861636f,    20.3811731565148f},
  { 130.124344291216f,    -62.9056646127018f},
  { 18.2474190537101f,    20.3811729886130f},
  { -68.6348318327801f,    -17.0687243103703f},
  { 49.8756558579031f,    62.9056644214068f},
  { 68.6348316582127f,    17.0687243084354f},
  { -49.8756555688743f,    -62.9056644946146f},
  { 111.365168318519f,    -17.0687242634348f},
  { -130.124344209978f,    62.9056643590092f},
  { -111.365168110473f,    17.0687242002251f},
  { 161.752580799423f,    -20.3811731737686f},
  { -18.2474191916171f,    -20.3811730380741f},
  { 2.71484106575056f,    48.4926781319369f},
  { 87.5997969787878f,    41.4504384176454f},
  { -177.285159050149f,    48.4926783149728f},
  { 41.4753914417279f,    1.79879023185710f},
  { 92.4002031412684f,    -41.4504386189539f},
  { -41.4753915917106f,    -1.79879025270390f},
  { -92.4002030805454f,    41.4504385125983f},
  { -138.524608439003f,    1.79879027718797f},
  { -87.5997968745335f,    -41.4504386683033f},
  { 138.524608649476f,    -1.79879018100771f},
  { -2.71484103403969f,    -48.4926780911917f},
  { 177.285158982351f,    -48.4926782083146f},
  { -98.1523160065715f,    -27.5438574820543f},
  { -152.216845561549f,    -7.22306125879088f},
  { 81.8476841627651f,    -27.5438573643616f},
  { -164.789178447502f,    -61.3658005156890f},
  { -27.7831545331737f,    7.22306140132871f},
  { 164.789178443534f,    61.3658007136397f},
  { 27.7831544823965f,    -7.22306144684801f},
  { 15.2108214755339f,    -61.3658004925845f},
  { 152.216845683231f,    7.22306141603186f},
  { -15.2108212260461f,    61.3658006465818f},
  { 98.1523159907921f,    27.5438572420303f},
  { -81.8476839310339f,    27.5438574201819f}};
 
/* Minimum T-design of degree 19 (204 points) */
const float __Tdesign_degree_19_dirs_deg[204][2] =
{ { -40.4827971398993f,    43.3558448910510f},
  { 124.512074059868f,    33.5755419701843f},
  { 139.517202845142f,    43.3558448775343f},
  { 38.8533744745300f,    -28.1674635453882f},
  { 55.4879258399038f,    -33.5755419872292f},
  { -38.8533744890089f,    28.1674635757744f},
  { -55.4879258707753f,    33.5755419610037f},
  { -141.146625425535f,    -28.1674634939008f},
  { -124.512074072873f,    -33.5755419765917f},
  { 141.146625395667f,    28.1674635597046f},
  { 40.4827970519826f,    -43.3558448545089f},
  { -139.517202930702f,    -43.3558447765375f},
  { 56.0057011667352f,    17.1841974993980f},
  { 20.4553778525436f,    32.2863965179037f},
  { -123.994298855438f,    17.1841975427728f},
  { 61.0525838868499f,    52.3805429894876f},
  { 159.544622091585f,    -32.2863964721300f},
  { -61.0525838977133f,    -52.3805429922499f},
  { -159.544622184482f,    32.2863964966156f},
  { -118.947416102450f,    52.3805429726830f},
  { -20.4553779060528f,    -32.2863965275596f},
  { 118.947416101692f,    -52.3805430422566f},
  { -56.0057011638433f,    -17.1841974992667f},
  { 123.994298849785f,    -17.1841975659790f},
  { -179.514728897842f,    -8.95189558912681f},
  { -93.0776196403050f,    -81.0350681242251f},
  { 0.485271044590434f,    -8.95189557283304f},
  { -98.9522115463824f,    -0.479359901942935f},
  { -86.9223806320116f,    81.0350680967773f},
  { 98.9522115996105f,    0.479359924611257f},
  { 86.9223801723002f,    -81.0350680963880f},
  { 81.0477884925503f,    -0.479359910390806f},
  { 93.0776194117918f,    81.0350681591717f},
  { -81.0477884388582f,    0.479359910640051f},
  { 179.514728907578f,    8.95189554407248f},
  { -0.485271033430437f,    8.95189552791142f},
  { 12.0366745311780f,    -13.5567796222345f},
  { -49.1452517185299f,    71.9460236947636f},
  { -167.963325421518f,    -13.5567796807998f},
  { 103.849922026142f,    11.6965010678641f},
  { -130.854748248662f,    -71.9460236355101f},
  { -103.849922019208f,    -11.6965010499568f},
  { 130.854748306321f,    71.9460237069809f},
  { -76.1500779540575f,    11.6965010382476f},
  { 49.1452517246089f,    -71.9460236210567f},
  { 76.1500779677235f,    -11.6965010395382f},
  { -12.0366745072388f,    13.5567796452543f},
  { 167.963325445597f,    13.5567797059840f},
  { -13.6177687853505f,    -58.2047889412688f},
  { -98.3039108388766f,    30.8020093497657f},
  { 166.382231262410f,    -58.2047889609688f},
  { 148.931723642678f,    -7.12599043766624f},
  { -81.6960891547253f,    -30.8020093817807f},
  { -148.931723587907f,    7.12599046490582f},
  { 81.6960891391292f,    30.8020094073706f},
  { -31.0682763825774f,    -7.12599044471178f},
  { 98.3039108451470f,    -30.8020093261083f},
  { 31.0682764509820f,    7.12599044985374f},
  { 13.6177687363442f,    58.2047889110994f},
  { -166.382231242976f,    58.2047889260604f},
  { 65.2592668684524f,    -20.5490633099000f},
  { -22.4282240836465f,    23.0717596473609f},
  { -114.740733101132f,    -20.5490633088132f},
  { 131.850731121270f,    58.2577280834148f},
  { -157.571775811254f,    -23.0717596621340f},
  { -131.850731298332f,    -58.2577279909000f},
  { 157.571775790124f,    23.0717596613445f},
  { -48.1492689459914f,    58.2577280717716f},
  { 22.4282240971360f,    -23.0717596293833f},
  { 48.1492688583973f,    -58.2577279963523f},
  { -65.2592668455931f,    20.5490632830229f},
  { 114.740733145086f,    20.5490632899652f},
  { -135.391308878658f,    26.4960083481501f},
  { 144.631254301060f,    -39.5791364301515f},
  { 44.6086911773665f,    26.4960083352508f},
  { -54.9998265959725f,    -38.9394958301661f},
  { 35.3687456809888f,    39.5791363676049f},
  { 54.9998265626444f,    38.9394958381227f},
  { -35.3687457312500f,    -39.5791363951356f},
  { 125.000173427157f,    -38.9394958686094f},
  { -144.631254355751f,    39.5791363679164f},
  { -125.000173460926f,    38.9394958286948f},
  { 135.391308874058f,    -26.4960083937547f},
  { -44.6086911769571f,    -26.4960083422148f},
  { 114.949924840136f,    -4.74760500909852f},
  { -5.23368224859043f,    -24.8584988627303f},
  { -65.0500751920101f,    -4.74760499288687f},
  { -101.138255685242f,    64.6308294162604f},
  { -174.766317811030f,    24.8584988453073f},
  { 101.138255567901f,    -64.6308294291222f},
  { 174.766317773328f,    -24.8584988721886f},
  { 78.8617442781326f,    64.6308294673680f},
  { 5.23368223316436f,    24.8584988162044f},
  { -78.8617443485117f,    -64.6308294202555f},
  { -114.949924797503f,    4.74760502019486f},
  { 65.0500752381225f,    4.74760499991936f},
  { 35.8486173395199f,    52.6418633116691f},
  { 65.9114275005164f,    29.4621373645687f},
  { -144.151382639220f,    52.6418633114291f},
  { 31.7487031863914f,    20.8159390557746f},
  { 114.088572496823f,    -29.4621373762114f},
  { -31.7487031850602f,    -20.8159390525807f},
  { -114.088572500623f,    29.4621373751269f},
  { -148.251296867652f,    20.8159390403083f},
  { -65.9114275150986f,    -29.4621373406821f},
  { 148.251296825615f,    -20.8159390193568f},
  { -35.8486173588977f,    -52.6418633449108f},
  { 144.151382653085f,    -52.6418633878030f},
  { 86.4503159839449f,    11.5178574130264f},
  { 11.5394039344984f,    3.47811299112874f},
  { -93.5496840137305f,    11.5178573996117f},
  { 16.9004866502571f,    77.9546248709343f},
  { 168.460596138258f,    -3.47811298337902f},
  { -16.9004867221619f,    -77.9546248991060f},
  { -168.460596111272f,    3.47811298260875f},
  { -163.099513269263f,    77.9546248607774f},
  { -11.5394039093281f,    -3.47811299154152f},
  { 163.099513332859f,    -77.9546249203649f},
  { -86.4503159901669f,    -11.5178574116444f},
  { 93.5496840314420f,    -11.5178573868150f},
  { 135.239557049900f,    4.01664853175916f},
  { 5.69483356922942f,    -45.0978192046165f},
  { -44.7604429511609f,    4.01664859407937f},
  { -84.3522817714199f,    44.6210488255627f},
  { 174.305166377085f,    45.0978191925169f},
  { 84.3522818209917f,    -44.6210488088963f},
  { -174.305166498240f,    -45.0978191964870f},
  { 95.6477182624038f,    44.6210488702794f},
  { -5.69483363835931f,    45.0978192003566f},
  { -95.6477182517814f,    -44.6210488918365f},
  { -135.239557005999f,    -4.01664858322133f},
  { 44.7604430095175f,    -4.01664863014437f},
  { -129.844345684641f,    -18.1635402775425f},
  { -156.862821803731f,    -37.5012149238997f},
  { 50.1556542868047f,    -18.1635403296931f},
  { -117.115121676957f,    -46.8469614266862f},
  { -23.1371782327970f,    37.5012149248207f},
  { 117.115121614901f,    46.8469614192763f},
  { 23.1371781765387f,    -37.5012149223183f},
  { 62.8848783969846f,    -46.8469613590856f},
  { 156.862821718985f,    37.5012149202724f},
  { -62.8848784049570f,    46.8469613748204f},
  { 129.844345741672f,    18.1635402578975f},
  { -50.1556542410030f,    18.1635403103006f},
  { -74.0995232303200f,    32.8713230086832f},
  { 146.101745919219f,    13.3031224588686f},
  { 105.900476735914f,    32.8713230206360f},
  { 22.9747088726656f,    -53.8773163872051f},
  { 33.8982540672711f,    -13.3031224827402f},
  { -22.9747089674201f,    53.8773163832442f},
  { -33.8982540495291f,    13.3031225041922f},
  { -157.025291161850f,    -53.8773163302415f},
  { -146.101745928058f,    -13.3031224379725f},
  { 157.025291066549f,    53.8773163620209f},
  { 74.0995232337151f,    -32.8713230260657f},
  { -105.900476736100f,    -32.8713230683644f},
  { -119.920654767573f,    -5.64202479284406f},
  { -173.497291648383f,    -29.7610425696254f},
  { 60.0793452237798f,    -5.64202480225216f},
  { -101.202909567639f,    -59.6005156643046f},
  { -6.50270830937896f,    29.7610425765434f},
  { 101.202909449688f,    59.6005156740098f},
  { 6.50270832065502f,    -29.7610425545166f},
  { 78.7970904807001f,    -59.6005155822608f},
  { 173.497291620421f,    29.7610425883022f},
  { -78.7970905474922f,    59.6005156241448f},
  { 119.920654807640f,    5.64202480200863f},
  { -60.0793451699613f,    5.64202480527789f},
  { 73.1351626703152f,    16.1311872967927f},
  { 16.8160239465430f,    16.1821871118731f},
  { -106.864837344194f,    16.1311872926822f},
  { 45.0880197945698f,    66.8258807656198f},
  { 163.183976128393f,    -16.1821870964153f},
  { -45.0880199162156f,    -66.8258808054124f},
  { -163.183976133830f,    16.1821870986028f},
  { -134.911980145466f,    66.8258807597722f},
  { -16.8160239202286f,    -16.1821871244424f},
  { 134.911980086750f,    -66.8258808490522f},
  { -73.1351626743642f,    -16.1311872709203f},
  { 106.864837351405f,    -16.1311872661606f},
  { -11.6972412007216f,    -43.3797087092533f},
  { -102.108896696603f,    45.3753435662694f},
  { 168.302758743556f,    -43.3797086959446f},
  { 133.980267409617f,    -8.47368576575139f},
  { -77.8911033135351f,    -45.3753435838886f},
  { -133.980267393688f,    8.47368572892681f},
  { 77.8911033110979f,    45.3753436128045f},
  { -46.0197325747014f,    -8.47368572030878f},
  { 102.108896727441f,    -45.3753435680196f},
  { 46.0197326174467f,    8.47368569981079f},
  { 11.6972411587316f,    43.3797087026179f},
  { -168.302758831810f,    43.3797087184118f},
  { -24.1050869937083f,    3.72760403870489f},
  { 170.936389463879f,    65.6254155023735f},
  { 155.894913041978f,    3.72760403395435f},
  { 85.9174400505778f,    -24.0508636473787f},
  { 9.06361051045597f,    -65.6254155365736f},
  { -85.9174400449213f,    24.0508636535097f},
  { -9.06361054264494f,    65.6254155057437f},
  { -94.0825599392362f,    -24.0508636829675f},
  { -170.936389442212f,    -65.6254155366095f},
  { 94.0825599175670f,    24.0508636802220f},
  { 24.1050870259372f,    -3.72760401034628f},
  { -155.894913008243f,    -3.72760399794214f}};
 
/* Minimum T-design of degree 20 (216 points) */
const float __Tdesign_degree_20_dirs_deg[216][2] =
{ { 104.601925128729f,    -3.68269227044959f},
  { -3.80525550883653f,    -14.5711050801146f},
  { -75.3980748712553f,    -3.68269227045763f},
  { -104.322150154107f,    74.9506325254330f},
  { -176.194744491161f,    14.5711050801105f},
  { 104.322150154173f,    -74.9506325254441f},
  { 176.194744491153f,    -14.5711050800763f},
  { 75.6778498458485f,    74.9506325254389f},
  { 3.80525550882118f,    14.5711050800919f},
  { -75.6778498458492f,    -74.9506325254403f},
  { -104.601925128768f,    3.68269227044241f},
  { 75.3980748712369f,    3.68269227047015f},
  { 153.768474770232f,    -30.3270175342204f},
  { -52.9262789947920f,    -50.7384907165667f},
  { -26.2315252297731f,    -30.3270175342403f},
  { -123.110247235077f,    22.4275681615901f},
  { -127.073721005197f,    50.7384907165599f},
  { 123.110247235061f,    -22.4275681615786f},
  { 127.073721005201f,    -50.7384907165500f},
  { 56.8897527649198f,    22.4275681615975f},
  { 52.9262789947688f,    50.7384907165558f},
  { -56.8897527649381f,    -22.4275681615922f},
  { -153.768474770235f,    30.3270175342297f},
  { 26.2315252297398f,    30.3270175342289f},
  { 35.9931099488083f,    -39.7686413526156f},
  { -54.7721532822064f,    38.4544369321159f},
  { -144.006890051185f,    -39.7686413526327f},
  { 135.808213283634f,    26.8538854974352f},
  { -125.227846717788f,    -38.4544369321345f},
  { -135.808213283626f,    -26.8538854974234f},
  { 125.227846717813f,    38.4544369321259f},
  { -44.1917867163936f,    26.8538854974017f},
  { 54.7721532821843f,    -38.4544369320921f},
  { 44.1917867163770f,    -26.8538854973852f},
  { -35.9931099488081f,    39.7686413526122f},
  { 144.006890051227f,    39.7686413526415f},
  { 71.8181243527431f,    -25.4259475349729f},
  { -26.5821567459587f,    16.3683231733698f},
  { -108.181875647256f,    -25.4259475349581f},
  { 146.720082499332f,    59.0980968893182f},
  { -153.417843254058f,    -16.3683231734038f},
  { -146.720082499387f,    -59.0980968892868f},
  { 153.417843254019f,    16.3683231733929f},
  { -33.2799175006570f,    59.0980968893018f},
  { 26.5821567459460f,    -16.3683231733863f},
  { 33.2799175007043f,    -59.0980968892965f},
  { -71.8181243527681f,    25.4259475349455f},
  { 108.181875647262f,    25.4259475349649f},
  { -136.553309024926f,    26.5218051743481f},
  { 144.031174024577f,    -40.5123550309482f},
  { 43.4466909750663f,    26.5218051743684f},
  { -55.4956627592942f,    -37.9745276892037f},
  { 35.9688259753990f,    40.5123550309626f},
  { 55.4956627592931f,    37.9745276892040f},
  { -35.9688259754170f,    -40.5123550309794f},
  { 124.504337240699f,    -37.9745276891974f},
  { -144.031174024568f,    40.5123550309630f},
  { -124.504337240703f,    37.9745276891987f},
  { 136.553309024903f,    -26.5218051743490f},
  { -43.4466909750886f,    -26.5218051743638f},
  { -6.51647188097905f,    -1.07894020321228f},
  { -170.577727686183f,    83.3951916100318f},
  { 173.483528119024f,    -1.07894020316580f},
  { 91.0859545987182f,    -6.51531150975361f},
  { -9.42227231365960f,    -83.3951916100331f},
  { -91.0859545987667f,    6.51531150975609f},
  { 9.42227231372673f,    83.3951916100228f},
  { -88.9140454012564f,    -6.51531150977155f},
  { 170.577727686387f,    -83.3951916100274f},
  { 88.9140454012482f,    6.51531150977345f},
  { 6.51647188096395f,    1.07894020318976f},
  { -173.483528119033f,    1.07894020319893f},
  { -71.1275142926455f,    40.3810353657942f},
  { 138.050297322915f,    14.2645186119443f},
  { 108.872485707367f,    40.3810353658053f},
  { 20.8229498967013f,    -46.1206992229688f},
  { 41.9497026770528f,    -14.2645186119106f},
  { -20.8229498966960f,    46.1206992229519f},
  { -41.9497026770679f,    14.2645186119222f},
  { -159.177050103330f,    -46.1206992229406f},
  { -138.050297322956f,    -14.2645186119422f},
  { 159.177050103338f,    46.1206992229801f},
  { 71.1275142926223f,    -40.3810353658125f},
  { -108.872485707350f,    -40.3810353658089f},
  { -153.965515116410f,    -27.9742815167833f},
  { -129.569241451541f,    -52.5179675742976f},
  { 26.0344848836063f,    -27.9742815167699f},
  { -120.587933155882f,    -22.8070349941593f},
  { -50.4307585484472f,    52.5179675742717f},
  { 120.587933155880f,    22.8070349941496f},
  { 50.4307585484843f,    -52.5179675742662f},
  { 59.4120668441292f,    -22.8070349941230f},
  { 129.569241451543f,    52.5179675742836f},
  { -59.4120668441431f,    22.8070349941496f},
  { 153.965515116415f,    27.9742815167763f},
  { -26.0344848836226f,    27.9742815167530f},
  { -80.2345666344704f,    13.4760126044716f},
  { 166.333234244309f,    9.49404277183603f},
  { 99.7654333655448f,    13.4760126044987f},
  { 35.2909555217966f,    -73.4109005990371f},
  { 13.6667657556541f,    -9.49404277183004f},
  { -35.2909555217526f,    73.4109005990409f},
  { -13.6667657556718f,    9.49404277180524f},
  { -144.709044478302f,    -73.4109005990245f},
  { -166.333234244339f,    -9.49404277182330f},
  { 144.709044478216f,    73.4109005990569f},
  { 80.2345666344400f,    -13.4760126044968f},
  { -99.7654333655573f,    -13.4760126044823f},
  { 55.4258411798564f,    -9.00107370832261f},
  { -10.8894834060658f,    34.0892935061751f},
  { -124.574158820165f,    -9.00107370834749f},
  { 105.596487285914f,    54.4149524298600f},
  { -169.110516593985f,    -34.0892935061760f},
  { -105.596487285927f,    -54.4149524298770f},
  { 169.110516593966f,    34.0892935061904f},
  { -74.4035127140624f,    54.4149524298548f},
  { 10.8894834060485f,    -34.0892935062018f},
  { 74.4035127140993f,    -54.4149524298663f},
  { -55.4258411798645f,    9.00107370833931f},
  { 124.574158820128f,    9.00107370833328f},
  { 68.3153335856534f,    -7.14339480007468f},
  { -7.68115300267237f,    21.5079337786373f},
  { -111.684666414376f,    -7.14339480009472f},
  { 108.735829009062f,    67.2230290834693f},
  { -172.318846997362f,    -21.5079337786408f},
  { -108.735829009106f,    -67.2230290834936f},
  { 172.318846997345f,    21.5079337786427f},
  { -71.2641709909006f,    67.2230290834666f},
  { 7.68115300265523f,    -21.5079337786644f},
  { 71.2641709909482f,    -67.2230290834717f},
  { -68.3153335856545f,    7.14339480008368f},
  { 111.684666414342f,    7.14339480008680f},
  { -174.969151608304f,    36.1200320060754f},
  { 96.8522393339851f,    -53.5785859742491f},
  { 5.03084839167049f,    36.1200320060603f},
  { -53.7746004797745f,    -4.06202009701441f},
  { 83.1477606660237f,    53.5785859742662f},
  { 53.7746004797533f,    4.06202009702199f},
  { -83.1477606660565f,    -53.5785859742666f},
  { 126.225399520230f,    -4.06202009702366f},
  { -96.8522393339372f,    53.5785859742576f},
  { -126.225399520243f,    4.06202009701189f},
  { 174.969151608272f,    -36.1200320060616f},
  { -5.03084839169859f,    -36.1200320060754f},
  { -149.906407826552f,    16.2606931032710f},
  { 149.813145407035f,    -56.1601274346795f},
  { 30.0935921734429f,    16.2606931032798f},
  { -71.3701782091179f,    -28.7740165038951f},
  { 30.1868545929113f,    56.1601274346756f},
  { 71.3701782091094f,    28.7740165038888f},
  { -30.1868545929296f,    -56.1601274347022f},
  { 108.629821790888f,    -28.7740165038695f},
  { -149.813145407052f,    56.1601274346882f},
  { -108.629821790894f,    28.7740165038910f},
  { 149.906407826543f,    -16.2606931032760f},
  { -30.0935921734718f,    -16.2606931032870f},
  { 2.52384960625872f,    -51.4512271200113f},
  { -87.9904040024997f,    38.5045003504209f},
  { -177.476150393760f,    -51.4512271199885f},
  { 141.478324772432f,    1.57250294138216f},
  { -92.0095959974952f,    -38.5045003504335f},
  { -141.478324772458f,    -1.57250294137597f},
  { 92.0095959974981f,    38.5045003504403f},
  { -38.5216752275558f,    1.57250294136416f},
  { 87.9904040024888f,    -38.5045003504353f},
  { 38.5216752275388f,    -1.57250294135528f},
  { -2.52384960627135f,    51.4512271200002f},
  { 177.476150393775f,    51.4512271200177f},
  { 161.118570987041f,    -9.98113371764410f},
  { -28.5384349241665f,    -68.7281514711054f},
  { -18.8814290129620f,    -9.98113371768145f},
  { -100.536379000037f,    18.5851021633060f},
  { -151.461565075782f,    68.7281514710960f},
  { 100.536379000000f,    -18.5851021633009f},
  { 151.461565075802f,    -68.7281514710950f},
  { 79.4636209999824f,    18.5851021633233f},
  { 28.5384349241945f,    68.7281514710894f},
  { -79.4636209999861f,    -18.5851021633212f},
  { -161.118570987047f,    9.98113371765684f},
  { 18.8814290129454f,    9.98113371766005f},
  { 12.8381161367250f,    24.9726634007955f},
  { 64.4943057166319f,    62.1101091429154f},
  { -167.161883863252f,    24.9726634008075f},
  { 64.4676966669117f,    11.6202315990140f},
  { 115.505694283338f,    -62.1101091429170f},
  { -64.4676966669310f,    -11.6202315990073f},
  { -115.505694283325f,    62.1101091429139f},
  { -115.532303333088f,    11.6202315990016f},
  { -64.4943057166577f,    -62.1101091429204f},
  { 115.532303333060f,    -11.6202315989894f},
  { -12.8381161367529f,    -24.9726634008133f},
  { 167.161883863254f,    -24.9726634007839f},
  { 74.1348174889496f,    41.6486122381530f},
  { 42.7558348462444f,    11.7870638762109f},
  { -105.865182511039f,    41.6486122381531f},
  { 17.0865743937080f,    45.9530694773398f},
  { 137.244165153751f,    -11.7870638761928f},
  { -17.0865743937328f,    -45.9530694773589f},
  { -137.244165153753f,    11.7870638761900f},
  { -162.913425606246f,    45.9530694773475f},
  { -42.7558348462681f,    -11.7870638761989f},
  { 162.913425606243f,    -45.9530694773507f},
  { -74.1348174889504f,    -41.6486122381588f},
  { 105.865182511041f,    -41.6486122381280f},
  { 154.035881840976f,    1.26890773623963f},
  { 2.89632328150881f,    -64.0070432393520f},
  { -25.9641181590101f,    1.26890773621974f},
  { -88.5886963134671f,    25.9572763928128f},
  { 177.103676718535f,    64.0070432393631f},
  { 88.5886963134513f,    -25.9572763928294f},
  { -177.103676718576f,    -64.0070432393329f},
  { 91.4113036865553f,    25.9572763928366f},
  { -2.89632328146162f,    64.0070432393464f},
  { -91.4113036865597f,    -25.9572763928243f},
  { -154.035881841000f,    -1.26890773624989f},
  { 25.9641181589920f,    -1.26890773624060f}};
 
/* Minimum T-design of degree 21 (240 points) */
const float __Tdesign_degree_21_dirs_deg[240][2] =
{ { 24.8037137130410f,    -10.4640534970921f},
  { -23.7615514381126f,    63.2086065432396f},
  { -155.196286289587f,    -10.4640534884876f},
  { 101.500381898951f,    24.3641198026634f},
  { -156.238448590064f,    -63.2086065458284f},
  { -101.500381888658f,    -24.3641198041221f},
  { 156.238448559844f,    63.2086065503554f},
  { -78.4996181151217f,    24.3641197988060f},
  { 23.7615514173273f,    -63.2086065546655f},
  { 78.4996181039697f,    -24.3641197939936f},
  { -24.8037137007022f,    10.4640534915037f},
  { 155.196286295679f,    10.4640534868210f},
  { -134.641988338408f,    65.4373209186038f},
  { 108.014259287393f,    -16.9833470063578f},
  { 45.3580116803753f,    65.4373209229614f},
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  { 71.9857407057664f,    16.9833470000679f},
  { 17.8047381601855f,    17.2035374099490f},
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  { -162.195261838500f,    17.2035374025352f},
  { 134.641988352629f,    -65.4373209298950f},
  { -45.3580116114767f,    -65.4373209177246f},
  { 177.598859321494f,    54.8491444701208f},
  { 88.3102490381675f,    -35.1154409081831f},
  { -2.40114069350551f,    54.8491444641872f},
  { -35.1271676217506f,    1.38214105769103f},
  { 91.6897509798567f,    35.1154409144503f},
  { 35.1271676308592f,    -1.38214107563309f},
  { -91.6897509639350f,    -35.1154409011172f},
  { 144.872832376883f,    1.38214105394520f},
  { -88.3102490433253f,    35.1154409067993f},
  { -144.872832382919f,    -1.38214106461202f},
  { -177.598859332362f,    -54.8491444783476f},
  { 2.40114065608711f,    -54.8491444798977f},
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  { -72.3438463610700f,    41.1054465255977f},
  { 19.1683264546669f,    -45.8901283135983f},
  { 72.3438463541316f,    -41.1054465270478f},
  { -42.4789657380600f,    13.2111181856663f},
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  { -28.4751425050509f,    -10.8961540375005f},
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  { -33.7911316991742f,    21.6144180011898f},
  { 144.533534418273f,    50.5909094016008f},
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  { 64.5101777390638f,    -31.1352111476882f},
  { 35.4664656025411f,    -50.5909093960748f},
  { -64.5101777345804f,    31.1352111445890f},
  { -35.4664655736399f,    50.5909094048493f},
  { -115.489822254523f,    -31.1352111461926f},
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  { 33.7911316959830f,    -21.6144179901815f},
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  { -175.526802493543f,    -31.7437477517178f},
  { -97.1851235504065f,    -57.9752633407046f},
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  { -121.822006774074f,    -3.80297880236091f},
  { -82.8148764588498f,    57.9752633312572f},
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  { 1.68823277243644f,    70.5588431716103f},
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  { -178.311767230745f,    70.5588431660223f},
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  { -89.4042236487700f,    -19.4323788021388f},
  { 90.5957763503897f,    -19.4323787954717f},
  { -27.2815067583220f,    -27.8808314491943f},
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  { -120.763555353242f,    23.9009625165290f},
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  { 59.2364446451883f,    23.9009624998341f},
  { 27.2815067487963f,    27.8808314664501f},
  { -152.718493245622f,    27.8808314654532f},
  { 139.901804856188f,    -15.4407806825701f},
  { -23.2113006173074f,    -47.5046360327723f},
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  { 124.236481466870f,    -78.3697009269409f},
  { -80.3431888585603f,    -6.51249291997702f},
  { 99.6568111422229f,    -6.51249292210797f},
  { 6.25305021559283f,    24.6392950256081f},
  { 76.6413523791277f,    64.6277102501776f},
  { -173.746949786342f,    24.6392950270846f},
  { 65.2308926368024f,    5.68174387058010f},
  { 103.358647610018f,    -64.6277102549169f},
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  { -103.358647609088f,    64.6277102395408f},
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  { -76.6413524385702f,    -64.6277102366225f},
  { 114.769107372832f,    -5.68174386565954f},
  { -6.25305020304394f,    -24.6392950440344f},
  { 173.746949810513f,    -24.6392950534774f},
  { 51.4090024464058f,    -63.4544715386100f},
  { -68.6705283534937f,    16.1863550443443f},
  { -128.590997556725f,    -63.4544715401145f},
  { 162.692298810171f,    20.4452510722808f},
  { -111.329471638371f,    -16.1863550400168f},
  { -162.692298815208f,    -20.4452510670904f},
  { 111.329471642948f,    16.1863550327398f},
  { -17.3077011861304f,    20.4452510665979f},
  { 68.6705283570530f,    -16.1863550335289f},
  { 17.3077011789208f,    -20.4452510732108f},
  { -51.4090024537963f,    63.4544715440609f},
  { 128.590997552950f,    63.4544715477391f},
  { -50.6030753394785f,    28.8535490286561f},
  { 144.511670270974f,    33.7724670889798f},
  { 129.396924676242f,    28.8535490380526f},
  { 49.0388136434489f,    -42.5966719232101f},
  { 35.4883297409466f,    -33.7724671046099f},
  { -49.0388136542479f,    42.5966719106232f},
  { -35.4883297326542f,    33.7724670909314f},
  { -130.961186367338f,    -42.5966719056932f},
  { -144.511670245097f,    -33.7724670921865f},
  { 130.961186354940f,    42.5966719131738f},
  { 50.6030753326950f,    -28.8535490411630f},
  { -129.396924672948f,    -28.8535490533258f}};
 
/* Minimum T-design of degree 30 (480 points) */
const float __Tdesign_degree_30_dirs_deg[480][2] =
{ { 13.6960601261042f,    2.12849455078750f},
  { 22.3672529329788f,    3.26018326470744f},
  { 19.7822526888058f,    12.7245912054259f},
  { 31.4961835085632f,    0.749608973508380f},
  { 30.0922529861350f,    9.95347112317270f},
  { 28.9776077078097f,    18.9944686965084f},
  { 39.5201303606249f,    11.1641896255397f},
  { 41.7164394113011f,    3.08397032332731f},
  { 38.7165113655867f,    20.5789647432244f},
  { 40.2284760177905f,    31.2584018565766f},
  { 49.0148578232563f,    14.0296855277638f},
  { 47.6760670431202f,    23.5720687312074f},
  { 52.2116961020212f,    6.15820050294267f},
  { 58.0891457617985f,    17.1240137367092f},
  { 58.0975802885148f,    26.2928953884844f},
  { 62.2534167045455f,    8.20383864923332f},
  { 67.5870707270298f,    17.3445388644534f},
  { 70.5764372977999f,    6.57616823288140f},
  { 78.4367051268425f,    10.3495864631808f},
  { 83.9434226672775f,    2.68591230435371f},
  { 2.19072891002142f,    -13.6864264797006f},
  { 3.52477947518199f,    -22.3291001286183f},
  { 13.4942488344899f,    -19.2769243983019f},
  { 0.879107453588522f,    -31.4931791059370f},
  { 11.4655896703476f,    -29.5937488441603f},
  { 21.4786307841915f,    -27.2638302586611f},
  { 14.3507782613724f,    -38.6313588224717f},
  { 4.12836656345967f,    -41.6425085039365f},
  { 25.6968567837124f,    -35.8422505012108f},
  { 38.4871278890970f,    -33.5101544329916f},
  { 20.8564191950947f,    -47.0847603563625f},
  { 32.9430318528116f,    -42.6608163612897f},
  { 9.98667458383702f,    -51.7872993130739f},
  { 30.2361749043852f,    -54.2173413119525f},
  { 43.0733481971825f,    -49.5628776276434f},
  { 17.2061941935799f,    -61.1586471998043f},
  { 39.3220435694026f,    -61.9361924300299f},
  { 19.1195422289134f,    -69.5341786055489f},
  { 42.3358183079906f,    -74.5286602462756f},
  { 23.9710329455048f,    -83.3766051243163f},
  { 98.9210048264399f,    76.1426581989395f},
  { 98.5132622022133f,    67.4084710025918f},
  { 123.711134389156f,    66.6173911749998f},
  { 91.4346002282839f,    58.4958143382882f},
  { 109.290245299578f,    58.4513637344324f},
  { 125.394209196642f,    55.8097037544560f},
  { 107.230633468620f,    49.1831921823224f},
  { 94.6288352137224f,    48.1905665325417f},
  { 120.975597856623f,    46.9250864921666f},
  { 133.225165739314f,    40.7413878157755f},
  { 108.315447712762f,    39.5164001582652f},
  { 120.545915807373f,    38.1074343439095f},
  { 97.7745045532820f,    37.5323944976275f},
  { 109.948430323503f,    30.3423852744922f},
  { 120.198798808278f,    28.2811798041250f},
  { 99.2523132528176f,    27.4385806787638f},
  { 108.666953765664f,    21.3424856507812f},
  { 96.9692379986232f,    19.2906876046471f},
  { 100.559220052228f,    11.3726271758806f},
  { 92.7009664390342f,    6.04989888883805f},
  { -76.3039398738958f,    2.12849455078750f},
  { -67.6327470670212f,    3.26018326470744f},
  { -70.2177473111942f,    12.7245912054259f},
  { -58.5038164914368f,    0.749608973508380f},
  { -59.9077470138650f,    9.95347112317270f},
  { -61.0223922921903f,    18.9944686965084f},
  { -50.4798696393751f,    11.1641896255397f},
  { -48.2835605886989f,    3.08397032332731f},
  { -51.2834886344133f,    20.5789647432244f},
  { -49.7715239822095f,    31.2584018565766f},
  { -40.9851421767437f,    14.0296855277638f},
  { -42.3239329568798f,    23.5720687312074f},
  { -37.7883038979788f,    6.15820050294267f},
  { -31.9108542382015f,    17.1240137367092f},
  { -31.9024197114852f,    26.2928953884844f},
  { -27.7465832954545f,    8.20383864923332f},
  { -22.4129292729702f,    17.3445388644534f},
  { -19.4235627022001f,    6.57616823288140f},
  { -11.5632948731575f,    10.3495864631808f},
  { -6.05657733272249f,    2.68591230435371f},
  { -2.19072891002142f,    13.6864264797006f},
  { -3.52477947518199f,    22.3291001286183f},
  { -13.4942488344899f,    19.2769243983019f},
  { -0.879107453588522f,    31.4931791059370f},
  { -11.4655896703476f,    29.5937488441603f},
  { -21.4786307841915f,    27.2638302586611f},
  { -14.3507782613724f,    38.6313588224717f},
  { -4.12836656345967f,    41.6425085039365f},
  { -25.6968567837124f,    35.8422505012108f},
  { -38.4871278890970f,    33.5101544329916f},
  { -20.8564191950947f,    47.0847603563625f},
  { -32.9430318528116f,    42.6608163612897f},
  { -9.98667458383702f,    51.7872993130739f},
  { -30.2361749043852f,    54.2173413119525f},
  { -43.0733481971825f,    49.5628776276434f},
  { -17.2061941935799f,    61.1586471998043f},
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  { -166.505751165510f,    -19.2769243983019f},
  { -179.120892546411f,    -31.4931791059370f},
  { -168.534410329652f,    -29.5937488441603f},
  { -158.521369215808f,    -27.2638302586611f},
  { -165.649221738628f,    -38.6313588224717f},
  { -175.871633436540f,    -41.6425085039365f},
  { -154.303143216288f,    -35.8422505012108f},
  { -141.512872110903f,    -33.5101544329916f},
  { -159.143580804905f,    -47.0847603563625f},
  { -147.056968147188f,    -42.6608163612897f},
  { -170.013325416163f,    -51.7872993130739f},
  { -149.763825095615f,    -54.2173413119525f},
  { -136.926651802818f,    -49.5628776276434f},
  { -162.793805806420f,    -61.1586471998043f},
  { -140.677956430597f,    -61.9361924300299f},
  { -160.880457771087f,    -69.5341786055489f},
  { -137.664181692009f,    -74.5286602462756f},
  { -156.028967054495f,    -83.3766051243163f},
  { -81.0789951735601f,    76.1426581989395f},
  { -81.4867377977868f,    67.4084710025918f},
  { -56.2888656108444f,    66.6173911749998f},
  { -88.5653997717161f,    58.4958143382882f},
  { -70.7097547004225f,    58.4513637344324f},
  { -54.6057908033581f,    55.8097037544560f},
  { -72.7693665313804f,    49.1831921823224f},
  { -85.3711647862776f,    48.1905665325417f},
  { -59.0244021433773f,    46.9250864921666f},
  { -46.7748342606863f,    40.7413878157755f},
  { -71.6845522872380f,    39.5164001582652f},
  { -59.4540841926275f,    38.1074343439095f},
  { -82.2254954467180f,    37.5323944976275f},
  { -70.0515696764966f,    30.3423852744922f},
  { -59.8012011917224f,    28.2811798041250f},
  { -80.7476867471824f,    27.4385806787638f},
  { -71.3330462343361f,    21.3424856507812f},
  { -83.0307620013768f,    19.2906876046471f},
  { -79.4407799477720f,    11.3726271758806f},
  { -87.2990335609658f,    6.04989888883805f},
  { -98.9210048264399f,    -76.1426581989395f},
  { -98.5132622022133f,    -67.4084710025918f},
  { -123.711134389156f,    -66.6173911749998f},
  { -91.4346002282839f,    -58.4958143382882f},
  { -109.290245299578f,    -58.4513637344324f},
  { -125.394209196642f,    -55.8097037544560f},
  { -107.230633468620f,    -49.1831921823224f},
  { -94.6288352137224f,    -48.1905665325417f},
  { -120.975597856623f,    -46.9250864921666f},
  { -133.225165739314f,    -40.7413878157755f},
  { -108.315447712762f,    -39.5164001582652f},
  { -120.545915807373f,    -38.1074343439095f},
  { -97.7745045532820f,    -37.5323944976275f},
  { -109.948430323503f,    -30.3423852744922f},
  { -120.198798808278f,    -28.2811798041250f},
  { -99.2523132528176f,    -27.4385806787638f},
  { -108.666953765664f,    -21.3424856507812f},
  { -96.9692379986232f,    -19.2906876046471f},
  { -100.559220052228f,    -11.3726271758806f},
  { -92.7009664390342f,    -6.04989888883805f}};
 
/* Minimum T-design of degree 40 (840 points) */
const float __Tdesign_degree_40_dirs_deg[840][2] =
{ { 149.263603834783f,    -53.0060664811199f},
  { -164.365030657005f,    60.2080167597588f},
  { -114.133156395014f,    -22.4117838350371f},
  { 99.7994227322605f,    -5.21863546706097f},
  { -106.287016605210f,    -70.2090939724247f},
  { 154.363310133555f,    56.6615370152244f},
  { -24.1886191948301f,    -37.8476655192962f},
  { 145.913308751917f,    32.9908659694550f},
  { 30.1584949552393f,    31.9524129967228f},
  { -178.686993681972f,    -11.1793164384719f},
  { 95.0873822760472f,    25.3965414160564f},
  { -70.4240468864204f,    53.7720444422919f},
  { -94.0330048989651f,    -2.83751338514659f},
  { 114.353915132664f,    -63.4833127536594f},
  { 131.581019315399f,    8.21952951813733f},
  { -132.940913655637f,    39.2157096320986f},
  { 124.364778287929f,    -8.00246008797146f},
  { 67.3130907697372f,    -29.7820566125311f},
  { -163.043979850952f,    -7.50723653872003f},
  { 167.879987492863f,    -7.95180234835099f},
  { 44.0921698625726f,    -25.2905871681089f},
  { 31.5781658177062f,    60.0282132459340f},
  { -35.5498000646238f,    -3.60507288940253f},
  { -30.4944240768537f,    -45.7861265646663f},
  { 138.476918887805f,    -51.0190550805302f},
  { -39.6759162188722f,    12.9913367417341f},
  { 41.9794954535117f,    -6.08388687053162f},
  { -42.2620746238942f,    -14.7511416956518f},
  { -154.146027087023f,    2.47755771672502f},
  { 0.0625705952352197f,    48.7809279839986f},
  { 105.091553924230f,    -13.8676921795039f},
  { -1.36871600594072f,    -18.3598920706058f},
  { 71.9893843573992f,    -20.4620187149798f},
  { -177.335015058207f,    32.3794914148608f},
  { -158.856612739765f,    11.6979132966246f},
  { -122.925397131742f,    -17.9109112965780f},
  { 118.869502795247f,    7.69533758561870f},
  { -134.752179532797f,    57.5294033214029f},
  { -151.780426631651f,    -78.9096156385351f},
  { -95.7626451719474f,    18.9656135432167f},
  { 120.671252161945f,    -13.7558255086613f},
  { -40.4243419504315f,    18.8777830371654f},
  { 141.908713656985f,    -28.0394087488386f},
  { 35.8051353818043f,    -25.2313946559004f},
  { -168.817821457456f,    1.28808805920167f},
  { 100.579692918687f,    -64.1321186392502f},
  { 76.2080180841815f,    33.8374380889844f},
  { -144.826476401732f,    85.0701615892237f},
  { -101.626412581563f,    -23.9996224086939f},
  { 167.721029521791f,    -47.7598767470431f},
  { 129.855803342282f,    34.5535588711217f},
  { -166.014429537489f,    -54.8275910830078f},
  { -56.0219525477008f,    -53.2033822144056f},
  { -172.155740988996f,    16.8063417598105f},
  { -171.869308336958f,    -12.0017323058903f},
  { -33.3397486273608f,    -38.9854284838043f},
  { 63.8350743552927f,    -15.1654552210621f},
  { -4.42797677109172f,    35.4688197817794f},
  { -50.0251524443123f,    20.7240614349903f},
  { -121.210164186962f,    -24.6465135229038f},
  { 16.6861673909000f,    38.4698531326131f},
  { -8.15933074488397f,    -41.6898001127167f},
  { -19.5841943769194f,    40.5685249452216f},
  { 177.247280514400f,    25.8280223666138f},
  { 48.7809449181953f,    -0.0412302558525259f},
  { -136.522915872743f,    -69.6141590079244f},
  { -18.3647804513672f,    1.29903163608235f},
  { -50.3531920170481f,    -62.9985615621742f},
  { 147.592461816819f,    2.25039932569429f},
  { 167.483504268373f,    20.6838680219578f},
  { 21.0591189997961f,    -31.1448908269880f},
  { -171.228527088859f,    -28.5854008636956f},
  { -65.6813738256384f,    -22.2084036076950f},
  { 84.7045313345268f,    -9.75840459955865f},
  { -19.0550132238698f,    -5.44883907181121f},
  { 164.112452742443f,    -29.7014307878198f},
  { -27.8040071892610f,    46.0805128313995f},
  { 139.195516345974f,    -43.9994072574599f},
  { 141.149045353151f,    47.1920617550663f},
  { -6.61364075589592f,    -78.7448159660119f},
  { 115.484271121278f,    -4.59463012694014f},
  { -145.383029625808f,    11.4210789348729f},
  { -87.1554541976338f,    -4.02805202442754f},
  { 24.4440271458979f,    -10.6090655964160f},
  { 100.929879165434f,    -41.0609005548679f},
  { -138.105107262278f,    -31.8574725173498f},
  { 80.3346646541484f,    -33.9841135805965f},
  { 58.1893665188901f,    19.5575204637846f},
  { -65.6834250290337f,    -71.5011245649553f},
  { 56.3648061751115f,    -75.5369883084871f},
  { 55.8213137724635f,    40.4950119904576f},
  { 163.196089446938f,    25.1886426922989f},
  { -83.8153715099452f,    54.2918464978552f},
  { -26.2763399522643f,    36.9330763410585f},
  { 28.2117101755392f,    -28.0973806306467f},
  { -109.867882950281f,    48.5875728654897f},
  { 80.9459421723854f,    47.6630864203711f},
  { -68.6191645350763f,    45.6992947586867f},
  { -95.6664393081424f,    -64.0357211750186f},
  { 179.945186811529f,    41.2190420862713f},
  { 75.6570477065003f,    -14.6416703213570f},
  { -4.11665805433526f,    71.5909138286826f},
  { 68.5771923006971f,    16.8390616567175f},
  { -175.806351393131f,    -57.5229183609744f},
  { -119.856831742108f,    -65.9667217175294f},
  { 59.2636038347830f,    -53.0060664811199f},
  { 105.634969342995f,    60.2080167597588f},
  { 155.866843604986f,    -22.4117838350371f},
  { 9.79942273226048f,    -5.21863546706097f},
  { 163.712983394790f,    -70.2090939724247f},
  { 64.3633101335554f,    56.6615370152244f},
  { -114.188619194830f,    -37.8476655192962f},
  { 55.9133087519166f,    32.9908659694550f},
  { -59.8415050447607f,    31.9524129967228f},
  { 91.3130063180282f,    -11.1793164384719f},
  { 5.08738227604718f,    25.3965414160564f},
  { -160.424046886420f,    53.7720444422919f},
  { 175.966995101035f,    -2.83751338514659f},
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  { 41.5810193153988f,    8.21952951813733f},
  { 137.059086344363f,    39.2157096320986f},
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  { -120.671252161945f,    13.7558255086613f},
  { 40.4243419504315f,    -18.8777830371654f},
  { -141.908713656985f,    28.0394087488386f},
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  { -129.855803342282f,    -34.5535588711217f},
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  { 33.3397486273608f,    38.9854284838043f},
  { -63.8350743552927f,    15.1654552210621f},
  { 4.42797677109172f,    -35.4688197817794f},
  { 50.0251524443123f,    -20.7240614349903f},
  { 121.210164186962f,    24.6465135229038f},
  { -16.6861673909000f,    -38.4698531326131f},
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  { -48.7809449181953f,    0.0412302558525259f},
  { 136.522915872743f,    69.6141590079244f},
  { 18.3647804513672f,    -1.29903163608235f},
  { 50.3531920170481f,    62.9985615621742f},
  { -147.592461816819f,    -2.25039932569429f},
  { -167.483504268373f,    -20.6838680219578f},
  { 158.940881000204f,    31.1448908269880f},
  { -8.77147291114150f,    28.5854008636956f},
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  { -34.6169703741920f,    -11.4210789348729f},
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  { 99.6653353458516f,    33.9841135805965f},
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  { -175.883341945665f,    -71.5909138286826f},
  { 111.422807699303f,    -16.8390616567175f},
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  { -140.324083781128f,    -12.9913367417341f},
  { 138.020504546488f,    6.08388687053162f},
  { -137.737925376106f,    14.7511416956518f},
  { -25.8539729129769f,    -2.47755771672502f},
  { 179.937429404765f,    -48.7809279839986f},
  { 74.9084460757705f,    13.8676921795039f},
  { -178.631283994059f,    18.3598920706058f},
  { 108.010615642601f,    20.4620187149798f},
  { -2.66498494179317f,    -32.3794914148608f},
  { -21.1433872602348f,    -11.6979132966246f},
  { -30.7363961652170f,    -53.0060664811199f},
  { 15.6349693429946f,    60.2080167597588f},
  { 65.8668436049860f,    -22.4117838350371f},
  { -80.2005772677395f,    -5.21863546706097f},
  { 73.7129833947903f,    -70.2090939724247f},
  { -25.6366898664446f,    56.6615370152244f},
  { 155.811380805170f,    -37.8476655192962f},
  { -34.0866912480834f,    32.9908659694550f},
  { -149.841505044761f,    31.9524129967228f},
  { 1.31300631802821f,    -11.1793164384719f},
  { -84.9126177239528f,    25.3965414160564f},
  { 109.575953113580f,    53.7720444422919f},
  { 85.9669951010349f,    -2.83751338514659f},
  { -65.6460848673365f,    -63.4833127536594f},
  { -48.4189806846012f,    8.21952951813733f},
  { 47.0590863443629f,    39.2157096320986f},
  { -55.6352217120711f,    -8.00246008797146f},
  { -112.686909230263f,    -29.7820566125311f},
  { 16.9560201490481f,    -7.50723653872003f},
  { -12.1200125071370f,    -7.95180234835099f},
  { -135.907830137427f,    -25.2905871681089f},
  { -148.421834182294f,    60.0282132459340f},
  { 144.450199935376f,    -3.60507288940253f},
  { 149.505575923146f,    -45.7861265646663f},
  { -41.5230811121950f,    -51.0190550805302f},
  { 140.324083781128f,    12.9913367417341f},
  { -138.020504546488f,    -6.08388687053162f},
  { 137.737925376106f,    -14.7511416956518f},
  { 25.8539729129769f,    2.47755771672502f},
  { -179.937429404765f,    48.7809279839986f},
  { -74.9084460757705f,    -13.8676921795039f},
  { 178.631283994059f,    -18.3598920706058f},
  { -108.010615642601f,    -20.4620187149798f},
  { 2.66498494179317f,    32.3794914148608f},
  { 21.1433872602348f,    11.6979132966246f},
  { -59.2636038347830f,    53.0060664811199f},
  { -105.634969342995f,    -60.2080167597588f},
  { -155.866843604986f,    22.4117838350371f},
  { -9.79942273226048f,    5.21863546706097f},
  { -163.712983394790f,    70.2090939724247f},
  { -64.3633101335554f,    -56.6615370152244f},
  { 114.188619194830f,    37.8476655192962f},
  { -55.9133087519166f,    -32.9908659694550f},
  { 59.8415050447607f,    -31.9524129967228f},
  { -91.3130063180282f,    11.1793164384719f},
  { -5.08738227604718f,    -25.3965414160564f},
  { 160.424046886420f,    -53.7720444422919f},
  { -175.966995101035f,    2.83751338514659f},
  { -24.3539151326635f,    63.4833127536594f},
  { -41.5810193153988f,    -8.21952951813733f},
  { -137.059086344363f,    -39.2157096320986f},
  { -34.3647782879289f,    8.00246008797146f},
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  { -106.956020149048f,    7.50723653872003f},
  { -77.8799874928630f,    7.95180234835099f},
  { 45.9078301374274f,    25.2905871681089f},
  { 58.4218341822938f,    -60.0282132459340f},
  { 125.549800064624f,    3.60507288940253f},
  { 120.494424076854f,    45.7861265646663f},
  { -48.4769188878050f,    51.0190550805302f},
  { 129.675916218872f,    -12.9913367417341f},
  { 48.0205045464884f,    6.08388687053162f},
  { 132.262074623894f,    14.7511416956518f},
  { -115.853972912977f,    -2.47755771672502f},
  { 89.9374294047648f,    -48.7809279839986f},
  { -15.0915539242296f,    13.8676921795039f},
  { 91.3687160059407f,    18.3598920706058f},
  { 18.0106156426008f,    20.4620187149798f},
  { -92.6649849417932f,    -32.3794914148608f},
  { -111.143387260235f,    -11.6979132966246f},
  { 120.736396165217f,    53.0060664811199f},
  { 74.3650306570054f,    -60.2080167597588f},
  { 24.1331563950140f,    22.4117838350371f},
  { 170.200577267740f,    5.21863546706097f},
  { 16.2870166052097f,    70.2090939724247f},
  { 115.636689866445f,    -56.6615370152244f},
  { -65.8113808051699f,    37.8476655192962f},
  { 124.086691248083f,    -32.9908659694550f},
  { -120.158494955239f,    -31.9524129967228f},
  { 88.6869936819718f,    11.1793164384719f},
  { 174.912617723953f,    -25.3965414160564f},
  { -19.5759531135796f,    -53.7720444422919f},
  { 4.03300489896510f,    2.83751338514659f},
  { 155.646084867337f,    63.4833127536594f},
  { 138.418980684601f,    -8.21952951813733f},
  { 42.9409136556371f,    -39.2157096320986f},
  { 145.635221712071f,    8.00246008797146f},
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  { 102.120012507137f,    7.95180234835099f},
  { -134.092169862573f,    25.2905871681089f},
  { -121.578165817706f,    -60.0282132459340f},
  { -54.4501999353762f,    3.60507288940253f},
  { -59.5055759231463f,    45.7861265646663f},
  { 131.523081112195f,    51.0190550805302f},
  { -50.3240837811279f,    -12.9913367417341f},
  { -131.979495453512f,    6.08388687053162f},
  { -47.7379253761058f,    14.7511416956518f},
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  { 68.8566127397652f,    -11.6979132966246f},
  { -57.0746028682579f,    17.9109112965780f},
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  { 59.3287478380547f,    13.7558255086613f},
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  { 38.0912863430153f,    28.0394087488386f},
  { 144.194864618196f,    25.2313946559004f},
  { -11.1821785425438f,    -1.28808805920167f},
  { 79.4203070813131f,    64.1321186392502f},
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  { 12.2789704782094f,    47.7598767470431f},
  { 50.1441966577185f,    -34.5535588711217f},
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  { -7.84425901100403f,    -16.8063417598105f},
  { -8.13069166304214f,    12.0017323058903f},
  { -146.660251372639f,    38.9854284838043f},
  { 116.164925644707f,    15.1654552210621f},
  { -175.572023228908f,    -35.4688197817794f},
  { -129.974847555688f,    -20.7240614349903f},
  { -58.7898358130382f,    24.6465135229038f},
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  { 2.75271948559983f,    -25.8280223666138f},
  { 131.219055081805f,    0.0412302558525259f},
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  { -2.75271948559983f,    25.8280223666138f},
  { -131.219055081805f,    -0.0412302558525259f},
  { 43.4770841272566f,    -69.6141590079244f},
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  { 114.318626174362f,    -22.2084036076950f},
  { -95.2954686654733f,    -9.75840459955865f},
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  { -155.555972854102f,    -10.6090655964160f},
  { -79.0701208345658f,    -41.0609005548679f},
  { 41.8948927377216f,    -31.8574725173498f},
  { -99.6653353458516f,    -33.9841135805965f},
  { -121.810633481110f,    19.5575204637846f},
  { 114.316574970966f,    -71.5011245649553f},
  { -123.635193824889f,    -75.5369883084871f},
  { -124.178686227537f,    40.4950119904576f},
  { -16.8039105530620f,    25.1886426922989f},
  { 96.1846284900549f,    54.2918464978552f},
  { 153.723660047736f,    36.9330763410585f},
  { -151.788289824461f,    -28.0973806306467f},
  { 70.1321170497187f,    48.5875728654897f},
  { -99.0540578276146f,    47.6630864203711f},
  { 111.380835464924f,    45.6992947586867f},
  { 84.3335606918577f,    -64.0357211750186f},
  { -0.0548131884707396f,    41.2190420862713f},
  { -104.342952293500f,    -14.6416703213570f},
  { 175.883341945665f,    71.5909138286826f},
  { -111.422807699303f,    16.8390616567175f},
  { 4.19364860686896f,    -57.5229183609744f},
  { 60.1431682578916f,    -65.9667217175294f},
  { -21.0591189997961f,    31.1448908269880f},
  { 171.228527088859f,    28.5854008636956f},
  { 65.6813738256384f,    22.2084036076950f},
  { -84.7045313345268f,    9.75840459955865f},
  { 19.0550132238698f,    5.44883907181121f},
  { -164.112452742443f,    29.7014307878198f},
  { 27.8040071892610f,    -46.0805128313995f},
  { -139.195516345974f,    43.9994072574599f},
  { -141.149045353151f,    -47.1920617550663f},
  { 6.61364075589592f,    78.7448159660119f},
  { -115.484271121278f,    4.59463012694014f},
  { 145.383029625808f,    -11.4210789348729f},
  { 87.1554541976338f,    4.02805202442754f},
  { -24.4440271458979f,    10.6090655964160f},
  { -100.929879165434f,    41.0609005548679f},
  { 138.105107262278f,    31.8574725173498f},
  { -80.3346646541484f,    33.9841135805965f},
  { -58.1893665188901f,    -19.5575204637846f},
  { 65.6834250290337f,    71.5011245649553f},
  { -56.3648061751115f,    75.5369883084871f},
  { -55.8213137724635f,    -40.4950119904576f},
  { -163.196089446938f,    -25.1886426922989f},
  { 83.8153715099452f,    -54.2918464978552f},
  { 26.2763399522643f,    -36.9330763410585f},
  { -28.2117101755392f,    28.0973806306467f},
  { 109.867882950281f,    -48.5875728654897f},
  { -80.9459421723854f,    -47.6630864203711f},
  { 68.6191645350763f,    -45.6992947586867f},
  { 95.6664393081424f,    64.0357211750186f},
  { -179.945186811529f,    -41.2190420862713f},
  { -75.6570477065003f,    14.6416703213570f},
  { 4.11665805433526f,    -71.5909138286826f},
  { -68.5771923006971f,    -16.8390616567175f},
  { 175.806351393131f,    57.5229183609744f},
  { 119.856831742108f,    65.9667217175294f}};
 
/* Minimum T-design of degree 50 (1296 points) */
const float __Tdesign_degree_50_dirs_deg[1296][2] =
{ { 6.31750018785189f,    5.71545247841618f},
  { 9.33666137417181f,    0.764875955810381f},
  { 12.7366434704163f,    5.68658142485854f},
  { 15.2949620394255f,    0.0333725968431899f},
  { 17.9037567992250f,    7.39288805432145f},
  { 20.0145383651178f,    1.54090664969374f},
  { 17.5251570761378f,    12.7500898369804f},
  { 23.3660740997915f,    7.58337618937538f},
  { 25.2427126430236f,    1.44949797785652f},
  { 21.7325149417603f,    15.4969703568972f},
  { 26.3232402377679f,    11.3420388968073f},
  { 29.5127172272453f,    5.15038681388645f},
  { 26.4638989064965f,    18.2428054047352f},
  { 32.1994237734007f,    0.645828887361602f},
  { 32.8255254258234f,    9.45207104671435f},
  { 31.2765374113426f,    14.7605851234668f},
  { 27.2393828124950f,    24.4919598722384f},
  { 37.0067464683316f,    5.67319469384795f},
  { 37.8039482456071f,    0.211578413422824f},
  { 32.1675256474504f,    21.2033937416403f},
  { 36.7283958680624f,    16.6027707299358f},
  { 38.8165575377462f,    11.3206889735115f},
  { 34.2338114580427f,    27.3451993103093f},
  { 42.7221806617192f,    4.42815492425229f},
  { 38.0643720059691f,    22.5745832466480f},
  { 44.0399479534900f,    10.0771456172288f},
  { 42.6132955686271f,    16.7525752947323f},
  { 47.1140649940803f,    2.56161948787102f},
  { 44.3058607688132f,    22.1806218085542f},
  { 41.6941737998675f,    27.6814347266868f},
  { 49.0989023407907f,    10.2508584891005f},
  { 48.0164081682955f,    16.1958835812124f},
  { 51.8828613038781f,    5.84246705766425f},
  { 45.1152426096349f,    31.7947821823200f},
  { 49.0981004711244f,    25.6147724979923f},
  { 51.6557722489001f,    20.7251460716084f},
  { 54.0049846553049f,    14.9454498617205f},
  { 56.2717490234111f,    10.5495845833380f},
  { 51.6956193505213f,    30.4282286732420f},
  { 57.6601397157023f,    4.86945471142963f},
  { 56.5569775382357f,    24.5800546431214f},
  { 58.3971963902080f,    19.1974452067879f},
  { 62.2426248572200f,    9.90888883052971f},
  { 61.7491860990915f,    15.2099635536057f},
  { 63.1423170276076f,    3.90963003576066f},
  { 65.7329780396423f,    19.8351059344430f},
  { 67.6554935549511f,    10.7242893874799f},
  { 68.4409624396340f,    4.84946097246874f},
  { 69.1997547135081f,    15.9632840431089f},
  { 73.3731586388839f,    5.97265382890480f},
  { 73.7397506527837f,    11.8702529919968f},
  { 78.9600906047694f,    4.79287632116766f},
  { 79.0167878592892f,    10.7308534022379f},
  { 86.1003993367101f,    0.941320326013424f},
  { 5.75013893576308f,    -6.28596736411227f},
  { 0.775143746480118f,    -9.33582199237545f},
  { 5.82906101631532f,    -12.6729186634914f},
  { 0.0345980377159959f,    -15.2949593814911f},
  { 7.76463283854887f,    -17.7499507937437f},
  { 1.63989766580014f,    -20.0069914045751f},
  { 13.3489649253100f,    -17.0795632730803f},
  { 8.25189697987607f,    -23.1497498450146f},
  { 1.60244798458380f,    -25.2340688810457f},
  { 16.6194698858780f,    -20.9045698239642f},
  { 12.6142805124942f,    -25.7709637762776f},
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  { -122.825525425823f,    -9.45207104671435f},
  { -121.276537411343f,    -14.7605851234668f},
  { -117.239382812495f,    -24.4919598722384f},
  { -127.006746468332f,    -5.67319469384795f},
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  { -141.655772248900f,    -20.7251460716084f},
  { -144.004984655305f,    -14.9454498617205f},
  { -146.271749023411f,    -10.5495845833380f},
  { -141.695619350521f,    -30.4282286732420f},
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  { -153.142317027608f,    -3.90963003576066f},
  { -155.732978039642f,    -19.8351059344430f},
  { -157.655493554951f,    -10.7242893874799f},
  { -158.440962439634f,    -4.84946097246874f},
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  { 174.249861064237f,    6.28596736411227f},
  { 179.224856253520f,    9.33582199237545f},
  { 174.170938983685f,    12.6729186634914f},
  { 179.965401962284f,    15.2949593814911f},
  { 172.235367161451f,    17.7499507937437f},
  { 178.360102334200f,    20.0069914045751f},
  { 166.651035074690f,    17.0795632730803f},
  { 171.748103020124f,    23.1497498450146f},
  { 178.397552015416f,    25.2340688810457f},
  { 163.380530114122f,    20.9045698239642f},
  { 167.385719487506f,    25.7709637762776f},
  { 174.086782964664f,    29.3818529057923f},
  { 159.786684974861f,    25.0390330618349f},
  { 179.236800795051f,    32.1971317480184f},
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  { 165.590219694378f,    37.9252811999644f},
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  { 176.238809347288f,    47.0524578843549f},
  { 150.329320852004f,    40.3007054606959f},
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  { 161.458366643474f,    54.8474909165491f},
  { 136.541189688306f,    42.5819270586039f},
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  { 159.439678822644f,    60.6599421898286f},
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  { 171.397850803893f,    62.8801970376911f},
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  { 153.518961830454f,    65.3345680955193f},
  { 166.998965360721f,    67.9276564617882f},
  { 141.147565139300f,    63.9975877642549f},
  { 159.915836297544f,    72.3614991600447f},
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  { 156.353275506898f,    77.9764340554490f},
  { 135.152518995700f,    74.6910173266745f},
  { 166.417774532483f,    85.9885662606724f},
  { -174.249861064237f,    -6.28596736411227f},
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  { -174.170938983685f,    -12.6729186634914f},
  { -179.965401962284f,    -15.2949593814911f},
  { -172.235367161451f,    -17.7499507937437f},
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  { -48.8168893785527f,    36.8547713099170f},
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  { -134.864966365994f,    -54.0081009249607f},
  { -99.3717754616855f,    -52.6225130948174f},
  { -90.3451714584523f,    -52.1955482039109f},
  { -126.079782661543f,    -52.1098199033771f},
  { -116.500200830029f,    -50.1804165363630f},
  { -107.712326587357f,    -49.8178833648037f},
  { -132.590454172503f,    -47.2534861883163f},
  { -96.5117703987492f,    -47.0929405560488f},
  { -123.991928381362f,    -46.6350359944150f},
  { -104.340362488158f,    -45.0534039865584f},
  { -113.969921713854f,    -44.8057592388772f},
  { -93.4940826230670f,    -42.8327805761788f},
  { -120.271511275129f,    -41.5033711197403f},
  { -128.262375692931f,    -41.3945881367105f},
  { -103.455811148776f,    -40.1135201030065f},
  { -111.342420447763f,    -39.9688401152677f},
  { -97.4103235661173f,    -37.8840017273009f},
  { -131.183110621447f,    -36.8547713099170f},
  { -122.387642121263f,    -36.1865484007360f},
  { -115.754138460121f,    -35.4673404514309f},
  { -108.258836785273f,    -34.5992892066947f},
  { -102.621763796510f,    -33.0840688505261f},
  { -126.814355003156f,    -32.3076388572271f},
  { -95.7578743135873f,    -32.2090209525075f},
  { -118.730384219651f,    -30.0772138863420f},
  { -112.235398627297f,    -29.6622959610919f},
  { -101.166813666368f,    -27.3084752395310f},
  { -107.152596737804f,    -27.1777031823352f},
  { -94.3806062016010f,    -26.7901812288672f},
  { -111.587537008777f,    -22.7435373722770f},
  { -101.572258060176f,    -21.9337711352895f},
  { -95.2123134646669f,    -21.4780231505450f},
  { -107.013876299185f,    -19.9632424259738f},
  { -96.2312677327183f,    -16.5339859327585f},
  { -102.349961185568f,    -15.9032151905555f},
  { -94.8828125811786f,    -11.0008233036095f},
  { -100.926300780106f,    -10.7888210685814f},
  { -90.9435043783131f,    -3.89907357767865f}};
 
/* Minimum T-design of degree 100 (5100 points) */
const float __Tdesign_degree_100_dirs_deg[5100][2] =
{ { 135.112963634543f,    -10.9070121585005f},
  { -149.773699959762f,    -5.04659267603735f},
  { 76.2994903762475f,    -14.0988534742932f},
  { 59.5000934898624f,    10.5432336322085f},
  { -162.921783362287f,    28.3536664014027f},
  { 103.675994855384f,    -0.837283967857134f},
  { -169.599206311779f,    61.9087522222797f},
  { 141.523979356684f,    -4.29946141054661f},
  { -53.9122841415104f,    -15.9665329498015f},
  { -44.0665165059163f,    29.1604953548073f},
  { -118.650072877756f,    17.7268104061847f},
  { 140.624682189535f,    -62.2336942496416f},
  { -169.826934955866f,    74.0579617493018f},
  { -174.924574979239f,    -11.0455351926701f},
  { 45.2805865752663f,    61.2546950762206f},
  { -52.8398089485056f,    -34.1298689414046f},
  { 8.37903274878709f,    56.3151333517369f},
  { 15.0708229219679f,    -17.9772003446941f},
  { 39.6307406711233f,    10.0794925730507f},
  { -77.7927877665195f,    -20.2960272241656f},
  { 25.0032356032190f,    -1.95766547893131f},
  { 67.3904436399691f,    38.5957126032353f},
  { -74.3709844064322f,    1.48902498866737f},
  { 153.972693036858f,    68.0968933422460f},
  { 11.5374976072462f,    -50.9756729786897f},
  { 160.863428572808f,    14.3384241532246f},
  { -42.4124051947123f,    18.6753700967494f},
  { -50.9896057568714f,    -41.0940650650316f},
  { 133.085681837097f,    -3.31314533193323f},
  { 75.9449020542073f,    -43.5615361963055f},
  { -89.5550411564168f,    -3.71469119237678f},
  { -100.068996746674f,    73.6712496717014f},
  { -69.5653596993217f,    10.9683268071274f},
  { -170.624755540029f,    28.4569306408453f},
  { 66.3585862216109f,    72.2456930119684f},
  { -175.847799424660f,    -16.9563286710119f},
  { 130.988991916770f,    -38.8614598365319f},
  { -101.419721936179f,    -29.3199254220964f},
  { 63.4955514785026f,    23.0836641602584f},
  { 133.731958269579f,    -36.6270675845425f},
  { -57.1932154799566f,    61.8343721338794f},
  { 105.427284784398f,    -71.1024301432785f},
  { -138.449889902351f,    -27.6247112732190f},
  { -97.8248798600467f,    -14.6232335898561f},
  { 91.7674701043864f,    -72.5720085009507f},
  { 72.0700065226631f,    26.1891998542538f},
  { 29.2392869531603f,    -50.7415662161816f},
  { -2.27224820848086f,    -37.7145121186939f},
  { -10.5942415758875f,    39.8919382717409f},
  { -26.6671098109331f,    20.2402883700549f},
  { -129.146515556787f,    17.3340836582898f},
  { -5.65262753529062f,    28.0146205608293f},
  { -131.919786468572f,    -38.1445272797611f},
  { -121.501149831346f,    54.1895126313824f},
  { -13.8150315427633f,    -55.9576047613440f},
  { 176.930100537907f,    2.50879170313885f},
  { 159.004251392201f,    -2.11751059077362f},
  { 67.7979604218379f,    -8.72202083169227f},
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  { 84.3137475790449f,    -54.2319226181052f},
  { 162.229940393571f,    31.8413016321649f},
  { 170.147741710903f,    56.3438477986082f},
  { -175.254976937647f,    62.1570805224970f},
  { 139.310804380514f,    13.5361475798077f},
  { -121.891318971798f,    -10.7571443198955f},
  { 169.930733448902f,    -21.4516408592173f},
  { -137.908374226866f,    46.0075503880130f},
  { -102.986336846238f,    51.8893074254159f},
  { 152.186177013984f,    24.2637249102616f},
  { 11.1758046110281f,    -1.89551322590027f},
  { -90.0384518384224f,    -42.1170394996486f},
  { -176.207841891074f,    -38.2830589232788f},
  { -18.4329067728413f,    -70.2683119004341f},
  { 14.9273195600812f,    59.0310601298339f},
  { -173.947522526029f,    32.6776339940352f},
  { 39.3443668860528f,    -83.3956608313680f},
  { -154.334448519806f,    10.0706577785609f},
  { -20.6676183595315f,    29.7617036593562f},
  { 91.3992762184414f,    56.2281936402504f},
  { -45.7170128409913f,    7.76547379335372f},
  { -46.5929096554972f,    12.3612310283071f},
  { 52.2326301779398f,    25.2322167823102f},
  { 30.9480453372373f,    -37.8335365805038f},
  { -67.7754472975621f,    -41.4824350497544f},
  { -121.622663270378f,    -36.1652844612277f},
  { 44.3024273032537f,    66.5168645780371f},
  { 13.2012905153634f,    -10.1513786149524f},
  { -156.788925214615f,    -36.4083262614618f},
  { -21.7656880977792f,    11.4030199226861f},
  { -150.544031001319f,    45.2804459416641f},
  { 40.7740550973078f,    81.8242264840177f},
  { 147.651930432843f,    48.4152460628433f},
  { 11.3902645519631f,    8.81031539170456f},
  { 2.12012801624649f,    -19.1764505638229f},
  { -98.4397593856159f,    -17.3333975924685f},
  { -133.652360391336f,    46.0284975695521f},
  { -88.7173718157719f,    -66.4839737154617f},
  { 29.8103490594183f,    -54.4217535403336f},
  { 81.8695792243455f,    -46.5737144954322f},
  { 108.061768690950f,    -23.7138578729902f},
  { 38.4624646824295f,    26.5066897550129f},
  { -57.6606717013683f,    -24.1151924049031f},
  { -66.3267842979266f,    11.6581605770965f},
  { 38.4236689661825f,    -63.0375977550849f},
  { 111.477794796451f,    53.5950034767582f},
  { 127.616208699265f,    15.8288698932269f},
  { -139.501248551419f,    33.2145194328305f},
  { 42.1854151197198f,    10.3907520484615f},
  { 0.265918112463301f,    43.2706646930475f},
  { 47.9175041513846f,    52.8094539594383f},
  { -113.607127117586f,    28.7484450397573f},
  { 145.794550168992f,    -44.6327009854747f},
  { -53.0727408154886f,    77.6452584179362f},
  { -104.788303664655f,    57.0908516652165f},
  { -135.276016179896f,    -68.1618521450301f},
  { 4.58132082330074f,    3.24912865780537f},
  { 53.7802800741766f,    -22.1490438705785f},
  { -169.202641381296f,    -66.3767367536038f},
  { -139.956863293524f,    -5.41063849273577f},
  { 176.133138353929f,    -65.6479368281171f},
  { 146.496474473878f,    19.8286430265157f},
  { 177.987095119279f,    -40.5394798045575f},
  { -24.1118524996585f,    18.8900312638985f},
  { 42.2721600695499f,    -41.5660665295109f},
  { 141.353624944245f,    2.75223296053804f},
  { -91.0886581164427f,    -34.2944117546512f},
  { 107.626606553871f,    -34.8032913279942f},
  { 111.395047104417f,    40.8672007033017f},
  { -2.82505762399135f,    -19.7198244574299f},
  { 11.2836678656487f,    23.7428658517588f},
  { -173.643054442712f,    -18.1617679198804f},
  { 9.93911038795652f,    14.6670767237319f},
  { 69.3074964014491f,    34.4462371509779f},
  { 54.2198079859001f,    13.6296588420586f},
  { -53.0338694846072f,    13.3721060678769f},
  { 169.822562239794f,    -53.6903989043287f},
  { -97.0508534370193f,    -11.8504348204251f},
  { -126.460372745046f,    10.9994261757589f},
  { 101.867324352530f,    -32.0075379439159f},
  { -20.1112261993772f,    55.6301997689592f},
  { 81.8352632490669f,    -49.5083501966845f},
  { -116.974019699633f,    4.77251182994046f},
  { 159.085952168148f,    19.0720411281375f},
  { -100.048704333476f,    -68.4817238967080f},
  { 28.5004678285019f,    -47.3738213427314f},
  { 161.353020607558f,    -52.8628694165051f},
  { 76.3730563347074f,    -3.83933840447496f},
  { 86.1303762447180f,    9.05463468442693f},
  { 31.2033572623228f,    -25.1449390379157f},
  { 135.913899919350f,    -28.9070533940600f},
  { 99.6492779404994f,    0.529958226635486f},
  { -175.491859312501f,    -32.7732969889126f},
  { 28.0363802341099f,    -17.7243797336922f},
  { -140.644058125827f,    15.4330450095360f},
  { 116.750800976684f,    -30.4623973105923f},
  { -47.7247241726644f,    42.7252754175174f},
  { -10.5357079412558f,    -11.7459707840831f},
  { -154.020503067389f,    -53.4397331430159f},
  { 150.028569631775f,    -15.0054189310047f},
  { -86.8879596387212f,    17.5716279469446f},
  { -45.9702444745094f,    -58.4387426510059f},
  { -163.814330226817f,    9.44481407742668f},
  { -28.1317161374850f,    -40.0695284547822f},
  { -171.527861353677f,    7.04791768450433f},
  { 83.3773413308710f,    -77.7289008657874f},
  { 66.5450896767189f,    -17.5923988007467f},
  { 117.994373003710f,    51.7861346813342f},
  { 150.182777916541f,    -18.1376195203615f},
  { -176.708223123409f,    -9.09511828098826f},
  { 25.0877181739368f,    13.2202611838159f},
  { -42.6797112768326f,    48.1924930229303f},
  { -99.3578796525260f,    -23.0239538217940f},
  { 37.4228223421450f,    30.0586950166840f},
  { -29.9728081870829f,    -23.0914937270495f},
  { -123.243583053886f,    -23.0891527918315f},
  { -71.2211750613129f,    -42.4515517411109f},
  { 2.62545428999846f,    -27.5889640319185f},
  { 178.058975142295f,    -33.4569630074206f},
  { -161.228313494596f,    18.4649545481562f},
  { -154.896518687260f,    -28.0109149983383f},
  { 146.700548403284f,    -47.2734490782859f},
  { -11.6774806557457f,    -26.3249094626074f},
  { -13.3952967939166f,    -4.01300593441310f},
  { 122.340996192320f,    -41.0003192831975f},
  { -174.780846833383f,    -57.4099403458448f},
  { -61.5514632789159f,    -12.7177049986953f},
  { -135.329159354338f,    -56.8168831376384f},
  { 10.1446844565427f,    -29.3576141818601f},
  { 135.849271712395f,    -51.4861448568760f},
  { -155.247947606974f,    -56.4907252814227f},
  { 130.378280165080f,    -35.6743184391846f},
  { 79.0495443916138f,    28.2131443600712f},
  { -169.730248335124f,    78.6220142607089f},
  { 14.9956517131916f,    -54.5754470511006f},
  { 144.925449207154f,    23.0464859965473f},
  { 11.7691818419248f,    -14.6126284138008f},
  { 4.10311000413954f,    22.2067900914894f},
  { -27.7577198373228f,    -77.4169475249471f},
  { -116.616363317282f,    54.3013683072767f},
  { -16.8443510360069f,    70.4016544068807f},
  { -67.3711932517415f,    -48.2129122837310f},
  { 30.0639068997333f,    -31.6760999125778f},
  { 45.0347523098179f,    -37.0292406739374f},
  { -112.878271116483f,    13.1804473656160f},
  { 68.5814790793370f,    23.0323278706626f},
  { 165.260495693782f,    1.67754359765327f},
  { -35.0354805751063f,    12.5293771941401f},
  { -112.940396516560f,    55.5579521467858f},
  { -69.2078422587628f,    16.6897874437738f},
  { -98.3986620346231f,    20.8480543580473f},
  { -63.6119340002199f,    0.199520664095598f},
  { -49.1872157527301f,    -23.1405240470593f},
  { -146.744222609815f,    25.5676733854070f},
  { -84.4099332090879f,    66.2685780710084f},
  { -62.5219881701826f,    22.0106922892138f},
  { -38.3082174260928f,    -64.9125112955009f},
  { 103.935283135809f,    -12.5626645297809f},
  { -116.294144919505f,    -41.9867299279931f},
  { 16.0029981519764f,    -10.7731207705523f},
  { 141.984287178435f,    -41.9398944224156f},
  { -56.5153160398744f,    33.1521948037556f},
  { -105.990618388314f,    -64.7174271624996f},
  { -21.5984673454286f,    -4.70073714019514f},
  { 162.580961147072f,    39.4811668817950f},
  { -99.4106761200345f,    2.05959953438535f},
  { -119.675306155206f,    5.65497446251534f},
  { -33.6860813623761f,    -1.71143871307232f},
  { -23.7138018621635f,    -34.6440375056665f},
  { 54.9816226479558f,    49.9741188328188f},
  { -149.242205963103f,    2.10454476083660f},
  { -102.036150963816f,    2.82362063438452f},
  { 27.1275572142944f,    22.2701295093799f},
  { 75.4212362581339f,    -47.0720331345554f},
  { -168.823753001481f,    45.5656544352614f},
  { -175.319127182704f,    53.6220571354719f},
  { 124.357880979874f,    -18.3503649952846f},
  { 141.956042666620f,    51.2854250417478f},
  { -19.6080400447921f,    0.590889931370865f},
  { 147.304059964494f,    -15.7984645909217f}};
 
/* Number of points in each minimum T-Design */
const int __Tdesign_nPoints_per_degree[21] =
{   2, 4, 6, 12, 12, 24, 24, 36, 48, 60, 70, 84, 94, 108, 120, 144, 156, 180, 204, 216, 240   };
 
/* Minimum T-design HANDLES */
const float* __HANDLES_Tdesign_dirs_deg[21] =
{ &__Tdesign_degree_1_dirs_deg[0][0],
  &__Tdesign_degree_2_dirs_deg[0][0],
  &__Tdesign_degree_3_dirs_deg[0][0],
  &__Tdesign_degree_4_dirs_deg[0][0],
  &__Tdesign_degree_5_dirs_deg[0][0],
  &__Tdesign_degree_6_dirs_deg[0][0],
  &__Tdesign_degree_7_dirs_deg[0][0],
  &__Tdesign_degree_8_dirs_deg[0][0],
  &__Tdesign_degree_9_dirs_deg[0][0],
  &__Tdesign_degree_10_dirs_deg[0][0],
  &__Tdesign_degree_11_dirs_deg[0][0],
  &__Tdesign_degree_12_dirs_deg[0][0],
  &__Tdesign_degree_13_dirs_deg[0][0],
  &__Tdesign_degree_14_dirs_deg[0][0],
  &__Tdesign_degree_15_dirs_deg[0][0],
  &__Tdesign_degree_16_dirs_deg[0][0],
  &__Tdesign_degree_17_dirs_deg[0][0],
  &__Tdesign_degree_18_dirs_deg[0][0],
  &__Tdesign_degree_19_dirs_deg[0][0],
  &__Tdesign_degree_20_dirs_deg[0][0],
  &__Tdesign_degree_21_dirs_deg[0][0]};
 
/* Sphere Covering (4 points) */
const float __SphCovering_4_dirs_deg[4][2] =
{ { -161.035517899469f,    32.3554996488327f},
  { -66.6980169311791f,    -31.3940764686032f},
  { 24.3822189717922f,    37.9922584373298f},
  { 109.291699421205f,    -39.0356145822630f}};
 
/* Sphere Covering (5 points) */
const float __SphCovering_5_dirs_deg[5][2] =
{ { 0.0f,    -90.0f},
  { -105.888330118127f,    0.0f},
  { 14.1136693674576f,    0.0f},
  { 134.112231106272f,    0.0f},
  { 0.0f,    90.0f}};
 
/* Sphere Covering (6 points) */
const float __SphCovering_6_dirs_deg[6][2] =
{ { 0.0f,    90.0f},
  { 0.0f,    -90.0f},
  { -77.7274544874475f,    0.0f},
  { 12.2716100561120f,    0.0f},
  { 102.272966430852f,    0.0f},
  { -167.727664946597f,    0.0f}};
 
/* Sphere Covering (7 points) */
const float __SphCovering_7_dirs_deg[7][2] =
{ { 148.510660497909f,    30.6406369680062f},
  { -65.2942703331086f,    -58.3442922781717f},
  { -14.5084372883027f,    1.52429691816604f},
  { -105.229428653727f,    25.3018162329772f},
  { 40.3665955403519f,    60.1892163784930f},
  { 74.7709922645724f,    -25.3018162329772f},
  { -176.958015026155f,    -33.5518355250659f}};
 
/* Sphere Covering (8 points) */
const float __SphCovering_8_dirs_deg[8][2] =
{ { -94.9906728547392f,    43.0342870344810f},
  { 109.916223417897f,    -54.2636868612500f},
  { 0.930999121308075f,    49.8685276148015f},
  { 128.147740458960f,    36.0636824989194f},
  { -105.372668102510f,    -38.6694945511744f},
  { -30.9385750214742f,    -27.3489944349796f},
  { -176.075660021653f,    1.82630297197950f},
  { 55.3849652663210f,    -9.88123013482618f}};
 
/* Sphere Covering (9 points) */
const float __SphCovering_9_dirs_deg[9][2] =
{ { -116.522426795756f,    85.0212072194629f},
  { 16.9658532716188f,    24.5094156023112f},
  { -91.1518556273627f,    -50.4202859715125f},
  { -132.834535223130f,    8.34455732828531f},
  { 149.163832384359f,    -47.7944203964279f},
  { 86.7057031371475f,    6.33576729855664f},
  { 156.577906253351f,    20.8482152914253f},
  { 22.0130384889262f,    -44.3005237617201f},
  { -54.6979888699592f,    10.8036921849868f}};
 
/* Sphere Covering (10 points) */
const float __SphCovering_10_dirs_deg[10][2] =
{ { 132.152715446924f,    -39.0184258484091f},
  { 62.9623321069262f,    9.21831796585981f},
  { 130.130174430113f,    26.4844011221272f},
  { -146.740220910955f,    51.0642905332395f},
  { 33.2573352183686f,    -51.0642905332395f},
  { 8.69635341449563f,    61.7190136914923f},
  { -158.434289509575f,    -13.6656163716653f},
  { -16.8890769270713f,    -0.849180748163393f},
  { -91.2893654981941f,    -53.5709808869368f},
  { -81.6980520077041f,    11.4454049155333f}};
 
/* Sphere Covering (11 points) */
const float __SphCovering_11_dirs_deg[11][2] =
{ { 111.113705209721f,    -75.3725979494598f},
  { 43.5510949656890f,    21.3770553363310f},
  { -124.165683782801f,    -29.8889163407945f},
  { 91.2721767643401f,    67.9871719702235f},
  { 16.3757067426341f,    -30.0705439618510f},
  { -58.3672105899770f,    -25.2989514440015f},
  { -112.895603952577f,    36.2183811036047f},
  { 102.267236852901f,    -12.7070579804114f},
  { 178.768561658768f,    -13.2055312621752f},
  { -34.5997753323602f,    32.6041633319195f},
  { 158.050407786838f,    33.4286495991128f}};
 
/* Sphere Covering (12 points) */
const float __SphCovering_12_dirs_deg[12][2] =
{ { 0.0f,    -31.7172246650570f},
  { -58.2812669207074f,    0.0f},
  { -90.0002104591497f,    58.2812669207074f},
  { 0.0f,    31.7172246650570f},
  { -121.719153997592f,    0.0f},
  { 90.0002104591497f,    -58.2812669207074f},
  { 180.0f,    -31.7172246650570f},
  { 121.719153997592f,    0.0f},
  { 90.0002104591497f,    58.2812669207074f},
  { 180.0f,    31.7172246650570f},
  { 58.2812669207074f,    0.0f},
  { -90.0002104591497f,    -58.2812669207074f}};
 
/* Sphere Covering (13 points) */
const float __SphCovering_13_dirs_deg[13][2] =
{ { 5.50772869303358f,    23.7794673713146f},
  { 142.546169850598f,    -67.9012283009539f},
  { -42.2682424623911f,    68.0788452174444f},
  { -93.0999121308075f,    -41.3142677334983f},
  { -45.8286022013340f,    4.83301359348752f},
  { 44.9027024044026f,    -2.11455803870982f},
  { -2.49288207083470f,    -45.6252021840626f},
  { -108.564043021388f,    19.9635684557433f},
  { -161.018329165615f,    -16.1694419363870f},
  { -179.788426534101f,    44.3910510933508f},
  { 135.991532674301f,    -4.76592023567770f},
  { 89.3470385727006f,    42.6813450326804f},
  { 85.5884354366424f,    -27.0178248293940f}};
 
/* Sphere Covering (14 points) */
const float __SphCovering_14_dirs_deg[14][2] =
{ { -45.9265779843014f,    -54.4951618104829f},
  { 126.881503731721f,    -63.0253574643906f},
  { -177.490865775626f,    -14.0007966818168f},
  { 79.0681757280536f,    -10.6495665380966f},
  { 175.880854371309f,    48.0665753491150f},
  { 131.052636480273f,    -0.752580063904336f},
  { 27.8898665935831f,    -35.8218943093742f},
  { 89.9371851016853f,    50.9783468639699f},
  { -22.7137658723712f,    4.77726480002129f},
  { -53.1200631021689f,    63.0253574643906f},
  { -125.798613498924f,    22.3717100686781f},
  { -75.3840571053624f,    2.88272255464171f},
  { -124.950635962130f,    -39.9712546617116f},
  { 27.5065578286406f,    26.5250811255815f}};
 
/* Sphere Covering (15 points) */
const float __SphCovering_15_dirs_deg[15][2] =
{ { 38.2804562082806f,    -30.8503395210240f},
  { -10.9944871307654f,    52.3288083870932f},
  { 107.773361264108f,    -72.5078089738057f},
  { 59.1464331913549f,    28.4645432620993f},
  { -104.931490600259f,    -11.1594989757630f},
  { -142.534710694695f,    -43.2348222627768f},
  { 156.658120344670f,    -21.2555882837633f},
  { 95.6495743191396f,    -14.9478959171680f},
  { 1.54996542738790f,    -1.22343677994285f},
  { -102.771439712616f,    43.3889479096670f},
  { -52.6920636292062f,    5.49340474815531f},
  { 131.132850571592f,    27.4269166951174f},
  { 147.645494227262f,    72.1869526085324f},
  { -161.528261603282f,    16.8449591768462f},
  { -44.6563305524964f,    -50.0312476286186f}};
 
/* Sphere Covering (16 points) */
const float __SphCovering_16_dirs_deg[16][2] =
{ { 64.8015266292961f,    -34.0268175372293f},
  { -127.517486884316f,    -50.0524470670385f},
  { 5.17552776341673f,    51.2487829432716f},
  { 170.202842621562f,    27.6291707967986f},
  { -73.0864963468878f,    32.0959497676385f},
  { -136.776484853630f,    66.7725014445461f},
  { 120.011739768102f,    -5.26416433432346f},
  { 178.069553148709f,    -22.2737342857108f},
  { -18.2194849273651f,    -56.5056707135969f},
  { 19.3224286829919f,    -5.99199262147815f},
  { -78.1800911456008f,    -18.1461463295883f},
  { -131.035447746419f,    8.38466437394447f},
  { 65.0421689032511f,    16.4519101293865f},
  { -30.7328831730222f,    1.12740905347892f},
  { 110.076651600534f,    52.6427892588249f},
  { 133.321549348991f,    -62.9623321069262f}};
 
/* Sphere Covering (17 points) */
const float __SphCovering_17_dirs_deg[17][2] =
{ { -128.010230588129f,    59.8855487470736f},
  { 80.3516011891467f,    -14.4746327783900f},
  { 153.363613022667f,    38.9754540137743f},
  { -161.763174299285f,    6.07449854397699f},
  { 141.457550039849f,    -11.9203869276968f},
  { -117.020900077519f,    -25.7091892253152f},
  { 29.5955619496875f,    17.4442730305530f},
  { -34.6633736476197f,    37.7447406698332f},
  { -62.7446081447765f,    -9.22462050160626f},
  { 29.6035833588194f,    -36.3616205523874f},
  { 108.844792341002f,    -60.0402473517590f},
  { -54.3095234848605f,    -64.1025181192365f},
  { -14.6734491333004f,    -10.8667175424512f},
  { -102.433394613489f,    22.3470728834875f},
  { -171.343028633873f,    -45.3072106077650f},
  { 93.5640079448634f,    25.1133131183791f},
  { 46.4164568991383f,    68.4398086283768f}};
 
/* Sphere Covering (18 points) */
const float __SphCovering_18_dirs_deg[18][2] =
{ { 123.294787934202f,    12.2653075203655f},
  { 123.638562611280f,    -42.2808475338840f},
  { 41.9342080678298f,    -42.1473483676185f},
  { -80.5865138851503f,    22.0485618722243f},
  { 76.5357022735754f,    -8.28095901302579f},
  { 127.815424937784f,    64.7614195836370f},
  { 19.5132236287704f,    6.30711940880010f},
  { -35.4890058304032f,    -84.8149424132158f},
  { -20.6104378064460f,    -38.0696077396724f},
  { -118.785610086522f,    58.5104500387597f},
  { -176.975203760009f,    31.7538939639454f},
  { -131.356304111693f,    1.40747082373887f},
  { -34.2703246001599f,    5.64907738109235f},
  { -13.8844862494052f,    53.6775510368312f},
  { 63.5753969477161f,    37.7773992641557f},
  { 171.148222983528f,    -12.3260410466494f},
  { -83.7893479599316f,    -28.6713810261415f},
  { -149.668035244074f,    -46.7957549595149f}};
 
/* Sphere Covering (19 points) */
const float __SphCovering_19_dirs_deg[19][2] =
{ { 179.049310978382f,    67.6090198254371f},
  { -76.3981924027440f,    -13.5000315688725f},
  { 37.0921417411792f,    -5.35864507474054f},
  { -113.766499801176f,    32.0397999037156f},
  { 90.4299288054978f,    -31.9716179260951f},
  { 143.514468524369f,    -9.92305605387073f},
  { -170.483591941176f,    17.3079090753119f},
  { 88.4589539902478f,    8.78859961951170f},
  { -36.4464183060668f,    63.9191716247946f},
  { 131.442247780962f,    36.6280459271233f},
  { -165.733771819542f,    -33.2378546533342f},
  { -125.775695187118f,    -14.4740598205949f},
  { 26.0208782658663f,    -52.9424461856783f},
  { 138.821944182247f,    -65.8901464400447f},
  { -21.0796902406581f,    -25.1178967807402f},
  { -0.924123627766505f,    19.1803351497994f},
  { -54.3416091213878f,    21.0779713672727f},
  { -84.5341930936017f,    -59.6563656290213f},
  { 57.0717530151862f,    46.9315459569609f}};
 
/* Sphere Covering (20 points) */
const float __SphCovering_20_dirs_deg[20][2] =
{ { -82.8611563318196f,    -56.0461585619020f},
  { 134.811239616331f,    23.6568544031566f},
  { -100.943704346148f,    -3.51280424194708f},
  { -143.606141771590f,    -43.0818425314769f},
  { 124.108388003288f,    73.1266033925470f},
  { 36.5730419787907f,    -6.54375097818913f},
  { -61.6846362237844f,    23.3130797260781f},
  { -116.436483126486f,    49.4559980023073f},
  { 179.387356077509f,    30.8812792419611f},
  { 7.71888741600245f,    -50.1349529895373f},
  { -48.4796779194044f,    -24.7540685808321f},
  { 83.6174606213923f,    23.1131174555774f},
  { 125.592348692676f,    -71.6770201708660f},
  { -146.642818085783f,    6.58443098164342f},
  { 115.055654840221f,    -22.2278976621003f},
  { -28.3384925471705f,    54.7570035228576f},
  { -9.34837938535451f,    2.50164832510020f},
  { 32.0180275075007f,    43.0268385831443f},
  { 71.0696849080273f,    -30.0315828317821f},
  { 165.750960553396f,    -22.0193410246727f}};
 
/* Sphere Covering (21 points) */
const float __SphCovering_21_dirs_deg[21][2] =
{ { 159.104650129878f,    -5.29229656206439f},
  { -154.377748320049f,    -15.7276914763411f},
  { -114.969711170951f,    60.4756952760584f},
  { 19.0531385192804f,    -14.8636711212838f},
  { 109.772983969114f,    -22.8787777173689f},
  { -175.399569823399f,    34.2617302332330f},
  { -124.240168296168f,    17.3038983707460f},
  { 83.7435113363211f,    23.5915372145116f},
  { -19.0794945778564f,    52.6107036222976f},
  { 32.0237570854520f,    33.8532113253047f},
  { 60.6361234586950f,    -62.9164954833157f},
  { -17.9278494096435f,    -50.9920978510530f},
  { 107.125918955610f,    69.2877861651705f},
  { -68.3022987575454f,    21.5139922493673f},
  { 128.308168641597f,    26.6368078956320f},
  { 59.8912783250249f,    -14.5067184149173f},
  { -118.413187519687f,    -62.8649292817539f},
  { 160.124515005211f,    -53.9371009180254f},
  { -104.358532805128f,    -17.8911801107551f},
  { -17.6740291064005f,    5.12218539269005f},
  { -56.7377186206249f,    -24.9190804258298f}};
 
/* Sphere Covering (22 points) */
const float __SphCovering_22_dirs_deg[22][2] =
{ { 71.9978765361392f,    43.7808510415365f},
  { -71.9978765361392f,    -9.65892251031542f},
  { 59.2151881267706f,    90.0f},
  { -120.785232791529f,    -90.0f},
  { 108.002544382160f,    -43.7814239993316f},
  { -107.996814804209f,    9.65949546811055f},
  { 36.0000841836599f,    -43.7819969571267f},
  { -180.0f,    9.65892251031542f},
  { 144.001482650230f,    43.7814239993316f},
  { 0.000325308247341427f,    -9.65892251031542f},
  { 0.000637759321760119f,    43.7814239993316f},
  { -144.001482650230f,    -9.65892251031542f},
  { -36.0000841836599f,    -43.7814239993316f},
  { 108.002544382160f,    9.65892251031542f},
  { -180.0f,    -43.7814239993316f},
  { -35.9995112258648f,    9.65892251031542f},
  { -144.001482650230f,    43.7819969571267f},
  { 71.9978765361392f,    -9.65949546811055f},
  { -71.9978765361392f,    43.7814239993316f},
  { 144.001482650230f,    -9.65892251031542f},
  { -108.002544382160f,    -43.7808510415365f},
  { 36.0006571414550f,    9.65892251031542f}};
 
/* Sphere Covering (23 points) */
const float __SphCovering_23_dirs_deg[23][2] =
{ { 68.5028339858412f,    -56.9485670892330f},
  { -53.8041747095551f,    -19.1768974030287f},
  { 126.193954377564f,    19.1768974030287f},
  { -18.5856049584536f,    7.72347107836350f},
  { -116.820364849224f,    37.7751074329752f},
  { 111.950223590612f,    61.9424672315933f},
  { -53.5176958119897f,    31.0778037656910f},
  { 71.6999384826712f,    31.2932358966602f},
  { -94.5838728201963f,    75.3955162612650f},
  { 93.2947177811520f,    -10.4243941246102f},
  { 50.8941220680856f,    -16.3430481483116f},
  { -179.862911047468f,    38.6328252522860f},
  { 166.742177538972f,    0.484664998901163f},
  { 179.817074423858f,    -71.8431779314539f},
  { -108.168702142748f,    -34.7246801316987f},
  { -46.9510265219953f,    -62.8248222360948f},
  { -167.630262121425f,    -33.4200552321858f},
  { -142.964429041043f,    2.40986048632024f},
  { 23.4603298794267f,    11.6602640887074f},
  { -92.6014388490437f,    2.59332157232113f},
  { 130.479678685142f,    -30.9093541739225f},
  { 8.96564357820712f,    52.7625374380073f},
  { 0.526966472915672f,    -35.2139860887404f}};
 
/* Sphere Covering (24 points) */
const float __SphCovering_24_dirs_deg[24][2] =
{ { 23.1314521050216f,    -10.3550662313994f},
  { -26.5777932427335f,    66.1651661817075f},
  { -26.5686259180114f,    -5.69256487774278f},
  { 137.005667971682f,    32.8448056058744f},
  { -0.620513292126682f,    28.7229472277033f},
  { 97.0876983849180f,    17.0197113043611f},
  { -11.8550697390519f,    -45.3564849781462f},
  { 91.6102218634673f,    65.7182591015054f},
  { -97.4429322178991f,    -1.18373080474028f},
  { 179.014933510674f,    15.5638255469337f},
  { 138.409414569753f,    -13.1705808366722f},
  { 103.269912994380f,    -30.4120268077490f},
  { 50.2501175063586f,    -56.5543721261830f},
  { -128.445678512428f,    -36.5094436635312f},
  { -175.262059952568f,    -26.5955549343826f},
  { -85.5024917673728f,    -70.8061243222671f},
  { -102.800087602372f,    43.6559462421979f},
  { 60.3668332949835f,    -9.40739403825299f},
  { 154.240238449218f,    -62.2060278173535f},
  { 47.4179871250269f,    34.3917916527277f},
  { -69.7346932453725f,    -26.3921549171111f},
  { -54.6848108406712f,    22.2319083666662f},
  { -141.262744389504f,    9.40166446030168f},
  { -158.422830353673f,    58.4416951033440f}};
 
/* Sphere Covering (25 points) */
const float __SphCovering_25_dirs_deg[25][2] =
{ { -101.585417076695f,    -9.81533998838613f},
  { 177.284600969379f,    46.2101920928912f},
  { -117.639694496261f,    36.2911467435863f},
  { -145.749003925379f,    9.78726505642472f},
  { -177.788803829094f,    -26.9886039818423f},
  { -74.1063612222207f,    -54.4092181412132f},
  { 136.060287609717f,    -23.4442870611630f},
  { -118.636641059788f,    81.6865928518015f},
  { -21.8067736826791f,    13.6822321477241f},
  { 14.9324260566995f,    -65.3859435803296f},
  { -70.8175834781698f,    17.2488944224134f},
  { -48.6550030047144f,    50.3102780748473f},
  { 166.335377504429f,    8.57259453074738f},
  { 46.0377317965568f,    -22.8455461652513f},
  { -8.56228129043502f,    -30.4893761100916f},
  { -54.5352688561420f,    -20.2964569347143f},
  { -133.166850744306f,    -35.9811765764206f},
  { 66.7381239768383f,    21.7345810004926f},
  { 100.852031098928f,    55.9143782690219f},
  { 94.0395629148220f,    -49.1053478316872f},
  { 122.836421698097f,    22.4335895105523f},
  { 92.0227514759615f,    -6.76605860269989f},
  { 173.451513319954f,    -68.3309466473020f},
  { 20.9725471329687f,    6.61250591360483f},
  { 19.8518416856928f,    49.2405658713381f}};
 
/* Sphere Covering (26 points) */
const float __SphCovering_26_dirs_deg[26][2] =
{ { 100.072808497550f,    3.17304026943450f},
  { -165.418645032220f,    -74.0777133324641f},
  { 128.543081337600f,    38.3560866372378f},
  { 171.543563862169f,    -38.9215959810320f},
  { 70.0555496106458f,    37.4731586749412f},
  { 26.1257295423753f,    -15.6623742876962f},
  { 67.8324733655382f,    -11.1142353099477f},
  { -56.7130814354343f,    31.1946871558977f},
  { -1.47737167474483f,    58.2698077648047f},
  { -94.6927348012712f,    3.87531463892635f},
  { 106.392532977843f,    -44.7720680271128f},
  { -9.65319293236411f,    -27.9368491327838f},
  { 165.172273180314f,    10.8019733116014f},
  { -51.7077221371714f,    -11.2007519370125f},
  { -166.959901501122f,    47.0123330060743f},
  { -37.6565051693831f,    -59.5990698495082f},
  { 49.4244853235751f,    -56.2592988616907f},
  { -130.903667453539f,    -30.3071755312400f},
  { -96.1079405552443f,    53.3452355156553f},
  { 134.977397376919f,    -10.8025462693965f},
  { -89.1694216562100f,    -39.7913459140406f},
  { -128.388382732915f,    16.2032464462997f},
  { -12.6199683955515f,    15.1495770610541f},
  { 106.759225966726f,    80.2140913183152f},
  { -161.774633455188f,    -1.90806404934467f},
  { 33.6990856784145f,    21.2154812381041f}};
 
/* Sphere Covering (27 points) */
const float __SphCovering_27_dirs_deg[27][2] =
{ { 101.642712856208f,    -10.3711090496630f},
  { 13.2857453534935f,    -25.0302342380851f},
  { -112.838308173064f,    -42.1169816044766f},
  { 148.527849231763f,    -18.0372843485134f},
  { 37.3230437326170f,    9.55292531821621f},
  { 100.502526843898f,    55.1414582033904f},
  { -140.821566887254f,    32.1807475213178f},
  { 130.846371674026f,    20.0603983231204f},
  { 79.1827672870798f,    20.6264806247096f},
  { -38.6752241291257f,    -55.1787004600739f},
  { -55.3379827271203f,    15.4228779293315f},
  { -27.7678265832202f,    50.9611581301159f},
  { -25.7584635956964f,    -14.5347933468787f},
  { 178.419057403738f,    6.01147318651260f},
  { 115.479643608617f,    -50.6517609207453f},
  { -73.7110203435804f,    -22.3694182374976f},
  { -94.1484248958969f,    40.3236237057171f},
  { -128.760805299750f,    80.1625251167535f},
  { 172.448837178475f,    43.7052206125792f},
  { -151.919759378938f,    -76.3810036688901f},
  { -142.677950143478f,    -9.55292531821621f},
  { 41.3469263278207f,    -57.3817231823520f},
  { 64.0165744499669f,    -23.0397788578007f},
  { -4.94898025122200f,    17.5136009237639f},
  { -175.181845861249f,    -39.7111318227222f},
  { 34.8157804211245f,    51.2728471706671f},
  { -102.708414355151f,    3.06016758379373f}};
 
/* Sphere Covering (28 points) */
const float __SphCovering_28_dirs_deg[28][2] =
{ { 130.771887160659f,    1.46413634967731f},
  { -43.4376493222531f,    -25.4828708962385f},
  { -65.9302534857038f,    62.4867771369676f},
  { -76.2549529539613f,    -7.86441869596568f},
  { 167.366701535665f,    -14.8476283030202f},
  { -138.294823010727f,    39.6463875918725f},
  { 86.5395453765595f,    8.84073877886860f},
  { -15.2773466493683f,    -1.99612766245628f},
  { -2.53917706068127f,    41.0959708135534f},
  { -98.3023689105954f,    -42.5123224831168f},
  { -153.180266528226f,    -35.7342317667192f},
  { 54.2218609422055f,    65.5922083865766f},
  { 11.2660691256574f,    -34.6226936441654f},
  { -35.7141782438896f,    -60.9627094019196f},
  { 143.915538980960f,    -44.7250854879121f},
  { 102.616741107930f,    -29.3772650297427f},
  { 55.1764086288934f,    -17.9186820849214f},
  { -158.428559931624f,    8.61556636538219f},
  { 164.049275901857f,    29.6620250539227f},
  { 24.8119373181403f,    8.12167674597942f},
  { -178.854505328038f,    68.0673860615418f},
  { -121.123277890656f,    -5.29424461856783f},
  { 113.222189895802f,    40.7367262760064f},
  { -47.6930068666897f,    21.9866824303502f},
  { -96.8241377991578f,    28.2748942319110f},
  { 64.5150477317307f,    -59.7365797203396f},
  { -170.386189116004f,    -74.5704570362767f},
  { 55.3660576590817f,    29.7296340737482f}};
 
/* Sphere Covering (29 points) */
const float __SphCovering_29_dirs_deg[29][2] =
{ { -174.671913423583f,    -23.7983749785539f},
  { -102.507879126856f,    17.4540133130703f},
  { -18.5202877698087f,    1.43600412193638f},
  { 7.18832849771131f,    35.8356452964573f},
  { -62.9852504187314f,    16.5269676005486f},
  { 48.9151258437038f,    -69.6773974658594f},
  { -60.0631656635642f,    -58.8484951378869f},
  { 97.9585942335169f,    -32.0965227254336f},
  { 106.679011875408f,    4.72208896435019f},
  { 68.8122311952119f,    4.51175615775767f},
  { -50.7210888139561f,    -20.8505071226058f},
  { -36.0293050312116f,    41.4145353476462f},
  { 48.2373167720640f,    32.5514512147675f},
  { -137.234851089735f,    -4.65946467734239f},
  { 51.5031762043097f,    -31.1121812333988f},
  { 94.9448362311287f,    44.1893699494647f},
  { 35.1102807278217f,    77.9509080275485f},
  { -179.238387050775f,    14.0099640065389f},
  { -92.5556022254332f,    -18.9987075287430f},
  { 170.237220089270f,    61.3408615467059f},
  { 143.646248817249f,    -13.0588540666217f},
  { 144.242124924185f,    28.7538869486404f},
  { 136.908265146510f,    -50.5211265434555f},
  { -146.344880032315f,    36.2791146298886f},
  { -161.957979949630f,    -66.8355268020105f},
  { -2.71427296287325f,    -37.7802640531314f},
  { -123.409379493228f,    -40.4221724464796f},
  { 23.1486408388755f,    -3.25995796695584f},
  { -90.9570499770182f,    57.3244274028389f}};
  
/* Sphere Covering (30 points) */
const float __SphCovering_30_dirs_deg[30][2] =
{ { 134.003369125197f,    37.1362594914043f},
  { -46.2205053332035f,    -58.1380274719246f},
  { -130.880749141734f,    -56.1893980106847f},
  { 75.3554092156059f,    -9.36213037243765f},
  { 14.2036237412931f,    41.4368807016563f},
  { -111.176730567185f,    51.0471017993856f},
  { -52.1150951295094f,    -14.3548845992076f},
  { 157.105027424872f,    4.74489268459640f},
  { 38.4689593228786f,    -25.6713740108365f},
  { 90.9742387108721f,    26.8104141075566f},
  { 143.015995242605f,    -36.1811388469212f},
  { 70.2102482153311f,    61.2950249230955f},
  { 30.0923163580660f,    -56.2558611149199f},
  { 49.3883889824818f,    18.4068421263728f},
  { 118.252759337051f,    -4.35356251052205f},
  { -26.0071272787832f,    16.0336509389410f},
  { -165.504588701490f,    0.431339816908338f},
  { -92.7045712521672f,    7.23473807911691f},
  { -66.7152056650331f,    26.2311537766794f},
  { 141.755488093317f,    -77.9165305598407f},
  { -89.3527681506519f,    -29.8350583080522f},
  { 91.8852416051301f,    -41.3177054802691f},
  { -12.6320005092493f,    -26.0082731943735f},
  { -130.451030795386f,    19.3757137579391f},
  { 162.553856056566f,    78.4837587770202f},
  { -178.487812339154f,    -34.7390040765770f},
  { -130.611458978022f,    -18.4068421263728f},
  { 13.0319250502506f,    2.23144142891650f},
  { -174.282302122894f,    40.4708738590657f},
  { -35.2380503161359f,    59.3641571535046f}};
 
/* Sphere Covering (31 points) */
const float __SphCovering_31_dirs_deg[31][2] =
{ { 106.959761195022f,    15.4400666631854f},
  { -12.7706562956709f,    41.9685855355377f},
  { -93.8504868424288f,    -28.3568271966147f},
  { 39.0917644461858f,    -24.7053671682460f},
  { -176.098578333459f,    53.8706378137903f},
  { -173.365569650685f,    9.57527067222632f},
  { -133.241335257673f,    -12.5580889536774f},
  { 144.832271453170f,    -8.08042378473000f},
  { 70.6285074057766f,    26.5657611290358f},
  { 106.100324502326f,    -21.3730446317651f},
  { -56.7657935525863f,    80.7412124898356f},
  { -43.2245090224644f,    -27.4114468346488f},
  { 38.3984855140775f,    53.6242659618840f},
  { 119.839852429563f,    -81.2797928172586f},
  { -174.815152872365f,    -22.8655996880809f},
  { -59.4329120889203f,    -0.266746231101106f},
  { 67.8496620993921f,    -3.25153548736742f},
  { -18.9694866811913f,    11.4494156200992f},
  { 146.178722271727f,    -48.3788373474613f},
  { 149.244046475677f,    26.9444862316172f},
  { -68.6804509023318f,    -60.5043431658149f},
  { 6.14382643718782f,    -54.5902728044746f},
  { -2.30649890007864f,    -18.1610432322617f},
  { -107.630121815325f,    47.0518670939383f},
  { -97.1679124762363f,    10.5217969497824f},
  { 114.333728018356f,    56.9537237093892f},
  { -140.678327438471f,    21.5472238014849f},
  { -57.0287811805514f,    36.5856470502836f},
  { 26.0495261556229f,    13.5756619978297f},
  { 78.2259277692113f,    -46.9028980672043f},
  { -143.571764303882f,    -49.9074887448704f}};
 
/* Sphere Covering (32 points) */
const float __SphCovering_32_dirs_deg[32][2] =
{ { 148.281477379857f,    -0.000106083135768472f},
  { 180.0f,    -20.9055110709384f},
  { 45.0001052295749f,    35.2644063747119f},
  { -45.0001052295749f,    -35.2644063747119f},
  { -135.000315688725f,    35.2644063747119f},
  { 135.000315688725f,    -35.2644063747119f},
  { -135.000315688725f,    -35.2644063747119f},
  { 135.000315688725f,    35.2644063747119f},
  { 44.9995322717797f,    -35.2638334169168f},
  { -45.0001052295749f,    35.2644063747119f},
  { -148.281477379857f,    -0.000273312327433305f},
  { 180.0f,    20.9049381131432f},
  { 6.47556900056856e-05f,    -58.2812669207074f},
  { -90.0002104591497f,    -69.0929805148260f},
  { -0.000445480415292166f,    58.2812669207074f},
  { 90.0002104591497f,    69.0929805148260f},
  { 180.0f,    -58.2812669207074f},
  { 90.0002104591497f,    -69.0929805148260f},
  { -90.0002104591497f,    31.7172246650570f},
  { -110.907440403473f,    -0.000228919557466569f},
  { 90.0002104591497f,    31.7177976228521f},
  { 69.0929805148260f,    0.000226461568525458f},
  { -90.0002104591497f,    -31.7177976228521f},
  { -69.0929805148260f,    -6.85142931417439e-05f},
  { 31.7172246650570f,    0.000273472755615942f},
  { -0.000250875300175982f,    20.9055110709384f},
  { -180.0f,    58.2812669207074f},
  { -90.0002104591497f,    69.0929805148260f},
  { 90.0002104591497f,    -31.7172246650570f},
  { 110.907440403473f,    6.78210142096355e-05f},
  { -31.7177976228521f,    0.000107681688016887f},
  { -0.000131035447746419f,    -20.9049381131432f}};
 
/* Sphere Covering (33 points) */
const float __SphCovering_33_dirs_deg[33][2] =
{ { -82.0762041524904f,    -28.1517083059579f},
  { 143.520198102320f,    -38.9645678156668f},
  { -179.748319488442f,    55.9923005291597f},
  { 96.2053433804165f,    -35.9531016444592f},
  { -132.118337979217f,    34.0308282417953f},
  { 140.827296465205f,    31.1901034935366f},
  { 155.449179396944f,    -3.15648178915522f},
  { 38.7789294900444f,    -1.34862805817893f},
  { 54.6555899931195f,    32.1744449855714f},
  { -125.580889536774f,    -34.4250232048453f},
  { 76.1289022390325f,    -4.32056014152251f},
  { 5.62524233681491f,    -19.6197937786648f},
  { -35.3457663816205f,    80.9474772960827f},
  { -95.7355179884093f,    60.0001403060998f},
  { -36.1261348985887f,    38.1945125390109f},
  { 48.9363252821236f,    -37.4622724768337f},
  { -78.9650433249301f,    -65.4088618921348f},
  { 0.839440465646169f,    -56.5939062140471f},
  { -166.604667668141f,    -59.6219881613135f},
  { 8.76453539211620f,    21.7998981891376f},
  { -171.646696265292f,    -22.3911906337126f},
  { -103.831411633608f,    2.06196051311681f},
  { -61.9481968095446f,    3.77246871470037f},
  { 118.138167778024f,    -4.47015942183117f},
  { 100.107185965257f,    61.8909010300315f},
  { 93.0769938190022f,    -72.9547160540077f},
  { -141.640896534291f,    -1.53707387699746f},
  { -174.505755662995f,    19.2278906467953f},
  { 19.2657058612739f,    54.1955048836294f},
  { -84.1675001047179f,    29.6608791383325f},
  { 97.5174167312661f,    25.2582714405472f},
  { -24.4733192612180f,    2.86994559581029f},
  { -39.0585328940682f,    -31.5906009923331f}};
 
/* Sphere Covering (34 points) */
const float __SphCovering_34_dirs_deg[34][2] =
{ { -145.754733503330f,    -23.4958532627248f},
  { -35.8786171310922f,    -38.2180038086113f},
  { 137.280687713345f,    43.6358927193684f},
  { -77.8936122480354f,    -46.4628664805438f},
  { -51.8005412999826f,    65.6036675424793f},
  { 63.0138983084879f,    -46.3385346390005f},
  { 144.637465802825f,    -22.2817556948426f},
  { -3.39133718937934f,    -75.6819951588305f},
  { -177.725778471630f,    -0.704967271128965f},
  { 76.2549529539613f,    -8.28668859097710f},
  { -24.6801570252602f,    29.1807405060128f},
  { -72.0609018936036f,    -9.43031235005822f},
  { -116.986522609811f,    46.3385346390005f},
  { 12.0074765125567f,    -38.6081880670954f},
  { -112.299727845641f,    -21.9746503166525f},
  { 128.021689744031f,    -64.4806702640229f},
  { 73.3099498869888f,    64.9275773442249f},
  { 151.117618465755f,    14.2013319101126f},
  { 174.626076799972f,    -39.7117047805174f},
  { 39.3937132042198f,    -12.9431165920053f},
  { 108.346319059239f,    -31.3522505495587f},
  { -4.84579055231894f,    -8.76682722329673f},
  { 114.236325193184f,    5.30381301374652f},
  { -132.674107040493f,    -62.1086249921812f},
  { 17.6499648790050f,    51.6647503025366f},
  { -169.727287651604f,    37.0239597635587f},
  { 55.0474931249890f,    24.1157935970564f},
  { -176.333491029462f,    74.6220232378384f},
  { -69.3164340549270f,    30.7242888060953f},
  { -41.2621285741414f,    -1.18029305796950f},
  { 15.3455286269888f,    14.6677195553491f},
  { -103.573580625799f,    10.3751197542289f},
  { 93.1171008646614f,    30.0132481823379f},
  { -139.566789315917f,    12.4572483817344f}};
  
/* Sphere Covering (35 points) */
const float __SphCovering_35_dirs_deg[35][2] =
{ { -167.991225532357f,    64.3030533475323f},
  { -134.713836791159f,    29.1005264146945f},
  { -1.52802114383439f,    -26.6591532496421f},
  { -25.6180889358894f,    1.56004948458221f},
  { -177.783074251143f,    -33.8434710427875f},
  { -10.8798955717392f,    36.0333157357775f},
  { -98.0273491689326f,    51.6578748089950f},
  { 13.4266929710957f,    8.24486267193255f},
  { -157.271185185460f,    -3.87073097656530f},
  { 136.747836963874f,    -0.991503464473890f},
  { 96.0334560418773f,    66.9501183610367f},
  { 139.159989281374f,    38.1738860583862f},
  { 105.223699075776f,    -25.1992567876487f},
  { 84.8321311470697f,    36.3501613964848f},
  { -42.2447511927907f,    -36.3799552018316f},
  { 147.966350592535f,    -36.4607422509451f},
  { -60.5730981012306f,    -3.48467201420615f},
  { 72.0265244258958f,    -4.37447547004432f},
  { 104.536149721619f,    13.6673352450507f},
  { 106.759225966726f,    -64.0566814956260f},
  { -176.751750219908f,    28.9779134465365f},
  { 49.3419794010762f,    12.1793638510959f},
  { -133.567921200898f,    -39.6641492835215f},
  { 33.1776940848455f,    -24.5747327909561f},
  { 35.0632981886210f,    45.5770737292716f},
  { -82.4715450311307f,    -62.1716503496456f},
  { 62.0169517449603f,    -40.2147617246422f},
  { -169.773124275214f,    -73.6365358302134f},
  { -89.0204526294760f,    -25.8879520573960f},
  { -53.7331279429589f,    32.9129875834950f},
  { -29.5222233519108f,    71.8374483535026f},
  { 7.38198823246553f,    -63.7071772405962f},
  { 165.241028115729f,    2.81459787280066f},
  { -92.9509431040735f,    14.9117995760748f},
  { -121.656128640128f,    -5.78687373082131f}};
 
/* Sphere Covering (36 points) */
const float __SphCovering_36_dirs_deg[36][2] =
{ { 42.0688531496856f,    39.0092585236870f},
  { -8.21277703540522f,    -31.9395322895677f},
  { -84.5399226715530f,    -29.0993804991043f},
  { -115.823418285696f,    -44.9628629728914f},
  { 99.9524873605721f,    -60.2235938462008f},
  { 132.582433793273f,    34.9103184573211f},
  { -43.9332578150413f,    -16.3040870182427f},
  { 22.2548266784714f,    71.6426427031581f},
  { -109.709958611650f,    -82.0819337304417f},
  { 80.6953758662252f,    41.7560181935441f},
  { 99.6660084630067f,    12.8159199614863f},
  { -149.186750696164f,    -25.2044134078049f},
  { -45.6223373950869f,    20.2448907331525f},
  { -90.9226725093103f,    27.9924260389115f},
  { 165.808256332909f,    14.3531657258223f},
  { -179.450381434974f,    -54.8360716985857f},
  { -52.0612370967671f,    -53.8202175278188f},
  { -117.954821283583f,    65.8672281282394f},
  { -117.347486020744f,    -4.31878397235761f},
  { -8.47404578998488f,    37.0067710297047f},
  { 22.6203737517649f,    -58.0062471790445f},
  { -11.2712257458136f,    0.512006544884806f},
  { 172.351434353303f,    -17.0586724344300f},
  { 132.771509865666f,    -3.38979020333249f},
  { -78.3405193282375f,    1.84572624123443f},
  { 59.7308501423883f,    -32.1423593490441f},
  { 130.726050537049f,    68.0501973276879f},
  { 24.0733947202167f,    11.8510590344859f},
  { 27.3885285228436f,    -16.7406808581324f},
  { -55.4634604842539f,    51.9071114498769f},
  { 135.790997446005f,    -35.3371720146935f},
  { -128.852478546971f,    30.4870842789111f},
  { -155.672632937045f,    8.25231112326925f},
  { 63.2201631147350f,    4.21083872375496f},
  { -174.883907807781f,    43.9298200682705f},
  { 95.2485038625481f,    -20.9536395257293f}};
 
/* Sphere Covering (37 points) */
const float __SphCovering_37_dirs_deg[37][2] =
{ { -41.8230542555744f,    31.6845660707345f},
  { 47.3142817641083f,    -30.2086267904775f},
  { -18.3249091616691f,    -22.4020768318201f},
  { -167.790690304062f,    36.1931709606190f},
  { -73.8771781041684f,    62.6758532093608f},
  { 78.1686319896982f,    -55.9441720743687f},
  { 20.0615442387106f,    19.6530253307824f},
  { -152.469798862263f,    -54.2132665752785f},
  { -14.9501877483486f,    10.2484960815050f},
  { 117.502184625429f,    -28.8535816049931f},
  { -110.523558680736f,    8.76625426550160f},
  { -51.7174624196886f,    -4.18923821487853f},
  { 80.1224180710943f,    19.1333526105987f},
  { -143.766569954226f,    11.5462454874764f},
  { 113.588882884686f,    9.77752477390750f},
  { -79.0968236178101f,    24.0218285186549f},
  { 163.092436383989f,    -30.6016758379373f},
  { -99.0242957324602f,    -48.9334604931480f},
  { -50.4936245692892f,    -42.9890233686657f},
  { -4.34949451017662f,    48.6733376541586f},
  { -119.559103109949f,    45.0258883303557f},
  { -42.0092655389920f,    -81.6980520077041f},
  { 178.390409513982f,    68.9783889557998f},
  { 145.027077103514f,    -2.58346669824488f},
  { 108.432262728508f,    48.3496164999097f},
  { -122.458269553311f,    -21.8932903097439f},
  { -81.5720012927753f,    -14.7181398413206f},
  { 15.5454908974895f,    -15.0940001549264f},
  { 146.362068766169f,    34.4857567311291f},
  { 176.568403725466f,    6.66120732619095f},
  { 44.3268798202961f,    74.4386767433966f},
  { 51.2636798459450f,    2.39164042843508f},
  { -159.941168510769f,    -19.6530253307824f},
  { 52.1529103439881f,    41.8196165088037f},
  { 144.929674278342f,    -61.1632446302154f},
  { 7.54241641510216f,    -53.9502789473135f},
  { 85.6915678397659f,    -17.5514161382425f}};
  
/* Sphere Covering (38 points) */
const float __SphCovering_38_dirs_deg[38][2] =
{ { 52.3058900752880f,    68.7377466818449f},
  { 18.7374387741633f,    -20.8860305059039f},
  { -3.43872079903666f,    -51.2304482938274f},
  { 154.853303290008f,    -30.2498797517269f},
  { 52.4680371313100f,    31.6140922619334f},
  { -109.618285364429f,    11.5622883057400f},
  { 4.39206527435484f,    49.0635219126427f},
  { 175.588645895792f,    69.1044396707286f},
  { 151.902570645084f,    9.40109150250655f},
  { -6.50880055268615f,    10.3648065139166f},
  { -34.7069184400496f,    37.4955040289513f},
  { -174.259383811089f,    34.6249854753459f},
  { 52.6026822131658f,    -45.1920460909437f},
  { -127.511757306365f,    -20.8785820545672f},
  { 173.560375301029f,    -57.6682020799174f},
  { -68.6575325905265f,    -57.8114415287001f},
  { -127.397165747339f,    45.1920460909437f},
  { 53.1166253553981f,    -82.0933928863444f},
  { 52.5310624887744f,    -8.28955337995275f},
  { 24.1610572628717f,    15.6302886511689f},
  { 139.738676654456f,    37.6610888317441f},
  { -75.1033077857483f,    -2.03210941199049f},
  { -80.6266209308094f,    34.5040913805733f},
  { 80.8386153150079f,    15.7093568268969f},
  { -127.614889709488f,    -58.0005176010932f},
  { -160.187540362676f,    -25.5670956921227f},
  { -145.313556001079f,    11.6132815495067f},
  { -179.862911047468f,    -1.90061559800797f},
  { -70.3191101964059f,    68.9669297998972f},
  { -20.1079538201162f,    -16.8037062155968f},
  { 108.592690911145f,    -51.0923654652009f},
  { 125.162630346328f,    -16.6449969063455f},
  { 86.3504693041664f,    -20.7937843008878f},
  { 100.519715577752f,    49.1867078385958f},
  { -46.8599262325695f,    9.23722557309913f},
  { -94.8417038280052f,    -25.6570500659583f},
  { 111.531964400166f,    10.5069000471090f},
  { -49.8358690204790f,    -30.4120268077490f}};
 
/* Sphere Covering (39 points) */
const float __SphCovering_39_dirs_deg[39][2] =
{ { 162.542396900663f,    38.2042528215282f},
  { -146.058401134749f,    43.9779485230615f},
  { -92.6759233624107f,    -42.7271816562909f},
  { -35.4764007589103f,    47.2558400690049f},
  { 93.9765375573576f,    25.3533824345389f},
  { -126.761182594743f,    -24.9328314129129f},
  { -61.7820390489567f,    -76.1117135051786f},
  { 163.877388563318f,    0.604470473863019f},
  { -134.163797307834f,    4.93763568687841f},
  { -145.577116586840f,    -54.9856136831148f},
  { 26.2420399747868f,    75.2465472345310f},
  { 3.67495129796910f,    -48.3948801657250f},
  { 78.6327278037542f,    -28.1803561957144f},
  { -96.9616476699892f,    -5.29985960496011f},
  { 13.8839132916101f,    42.6057146037231f},
  { -39.4000157399662f,    11.4803553410363f},
  { -26.0581205225498f,    -18.3037097232493f},
  { 33.3438518454334f,    12.3277599200348f},
  { -86.2072298553837f,    60.3267262493244f},
  { -65.7984731928238f,    -13.1115661837738f},
  { 111.961682746514f,    55.7430638882778f},
  { 59.3526979976020f,    42.4349731807742f},
  { 165.189461914168f,    -36.9958848315973f},
  { 40.8513178350326f,    -24.5712950441854f},
  { -6.25669912282859f,    17.1125304671723f},
  { 114.688961851337f,    -43.1947152171176f},
  { 64.6067209789516f,    5.10625716598541f},
  { -46.7040817122939f,    -43.6496437064515f},
  { 131.528191450232f,    21.0688040425506f},
  { -110.237079783170f,    28.2737483163207f},
  { -175.898043105163f,    71.0238482844169f},
  { -164.014898434149f,    -20.0455014204470f},
  { 144.797893985462f,    -69.8836622721065f},
  { -72.6453188446371f,    23.9083828752190f},
  { 133.338738082845f,    -14.8149697086977f},
  { 7.25364568635622f,    -12.5901745902047f},
  { 102.003676267140f,    -4.36851670897496f},
  { 55.9802684154620f,    -60.7220671279647f},
  { -165.418645032220f,    15.8554610646553f}};
 
/* Sphere Covering (40 points) */
const float __SphCovering_40_dirs_deg[40][2] =
{ { 34.0296823262050f,    -14.9238316897726f},
  { -133.035070451426f,    29.7044239307624f},
  { -106.896735837558f,    -59.7193909864857f},
  { 107.830657043621f,    -54.6005860447869f},
  { 68.4971044078899f,    38.4408843909172f},
  { -127.964393964518f,    -4.12896305483076f},
  { -176.843423467129f,    -25.7974247257653f},
  { 31.5241378880979f,    57.3358865587415f},
  { -101.906273441968f,    49.1580599488392f},
  { -33.7689865294205f,    11.8923119957354f},
  { -60.3038079375191f,    80.4318152804650f},
  { 44.4323040546002f,    -51.0986680009473f},
  { -38.3744212866820f,    51.1697147675436f},
  { -165.917118313984f,    59.4902078684334f},
  { 132.152715446924f,    4.39538842956660f},
  { -138.655786421659f,    -36.8692611588733f},
  { 162.668447615592f,    2.05055865299370f},
  { -31.3339159001145f,    -18.5718539713705f},
  { 92.5556022254332f,    5.56290452870468f},
  { -171.480538504704f,    25.4834438540336f},
  { 109.526612117208f,    31.1488505322872f},
  { -62.8190926581435f,    -39.2957374212524f},
  { 108.162972564797f,    -20.3755251104423f},
  { -98.4570675152807f,    -23.0661349163767f},
  { 144.511415087896f,    -30.8096595175698f},
  { -97.7007632257080f,    12.1891041336131f},
  { 62.3091602204770f,    4.72781854230150f},
  { 150.584767716283f,    37.4811800840731f},
  { 2.78159550380112f,    -34.4657032082995f},
  { 175.027147256564f,    -59.5532332258978f},
  { 30.9156567096690f,    20.2059296030836f},
  { 35.3302965211520f,    -85.2102832918560f},
  { -66.8813634256210f,    -5.26731560219668f},
  { -25.7349723260961f,    -57.8114415287001f},
  { -65.6036675424793f,    28.9360875274920f},
  { 1.57534745771220f,    -0.258535745896881f},
  { -158.044678208886f,    -1.69933552457851f},
  { 113.256567363510f,    65.2999999110599f},
  { -4.71257786495102f,    33.4527138265082f},
  { 71.5165919882294f,    -28.2817697254526f}};
 
/* Sphere Covering (41 points) */
const float __SphCovering_41_dirs_deg[41][2] =
{ { 42.8778695564103f,    26.0013977008319f},
  { -87.8859961951170f,    42.3765314856708f},
  { 1.92679976924545f,    34.5356040593055f},
  { -47.9875071733870f,    -18.7242607448753f},
  { -10.1442177627912f,    -18.4698674838372f},
  { -77.7675615331066f,    -79.5380011200609f},
  { 129.465543387761f,    38.5594866545093f},
  { -124.274545763876f,    71.3676229614953f},
  { 38.3612432573940f,    -7.37797752789961f},
  { -114.746257630850f,    -23.1990611248470f},
  { 119.811204539806f,    68.2793804457402f},
  { 134.003369125197f,    -1.13777958957079f},
  { 64.6983942261726f,    -30.2791005992786f},
  { -27.6045336116079f,    10.4559068033424f},
  { 20.2454636909476f,    -33.4355250926543f},
  { 170.351811648296f,    -11.8361621318125f},
  { 72.2327892321429f,    4.41372307901078f},
  { -131.075554792078f,    -50.5898814788712f},
  { 36.2647906850103f,    60.4470473863019f},
  { 157.632148596392f,    19.4118100990323f},
  { -76.8450994829460f,    -44.7967052123034f},
  { -130.605729400071f,    3.64338132345739f},
  { 149.702412711781f,    -70.4165130215782f},
  { -165.315512629096f,    14.1262744389504f},
  { 177.072606585181f,    -46.1076326475627f},
  { -155.139782187573f,    -19.8644467571856f},
  { 10.0250425414040f,    5.28977554776581f},
  { -101.144239574444f,    14.4333798171406f},
  { 99.8780028472051f,    -18.2395384501946f},
  { -179.564972994000f,    47.5188276969700f},
  { -134.960208643065f,    37.0720882183497f},
  { -30.2951434175423f,    70.4165130215782f},
  { -62.3263489543310f,    13.7698946903791f},
  { -40.8776738936086f,    43.2250819802596f},
  { 137.257769401540f,    -31.1717688440924f},
  { 80.6151617749068f,    39.0224365529750f},
  { 107.080082332000f,    14.6700113865296f},
  { -26.2133920850303f,    -49.5648599833821f},
  { 100.989540969759f,    -52.9716670332300f},
  { -84.4539790022834f,    -11.7674071963968f},
  { 37.1735017480878f,    -61.6044221324661f}};
 
/* Sphere Covering (42 points) */
const float __SphCovering_42_dirs_deg[42][2] =
{ { 108.856251496905f,    -64.2342984121166f},
  { -132.937667626254f,    -45.9706957345265f},
  { 17.1503456816509f,    55.2549038468263f},
  { -6.91044396707286f,    -7.18259891976000f},
  { -18.8932832944389f,    27.5294761404458f},
  { -59.4157233550664f,    82.8898042215762f},
  { -70.5253750026530f,    -15.1770790352204f},
  { 152.532824219728f,    -18.7603570859685f},
  { -120.653452498649f,    17.9977502606494f},
  { 94.6067911320015f,    -9.01663682197377f},
  { -82.9929366246997f,    -44.7296691502731f},
  { 5.02014160937725f,    -33.2773887411982f},
  { 150.498824047013f,    65.9474422195578f},
  { -108.839062763051f,    -17.7823181296802f},
  { -154.366289164146f,    21.9345432709933f},
  { 44.9422364922666f,    -31.6404483205095f},
  { -137.847915930525f,    52.9808343579521f},
  { -169.005360829739f,    -27.2813854151542f},
  { 172.185276592715f,    38.9078449939488f},
  { 123.277599200348f,    37.5997823476652f},
  { 122.223356857307f,    3.89427954194518f},
  { 13.6988479237829f,    22.9549811041213f},
  { 75.6476176911226f,    57.7140387035278f},
  { -126.102281130343f,    -77.2289812056837f},
  { -90.1148020181759f,    10.7693147172790f},
  { 168.575642483391f,    -52.7046687006990f},
  { 152.641686200803f,    14.7588198447749f},
  { -37.9005851901088f,    -30.9506071351719f},
  { -94.1197770061403f,    46.8685205994965f},
  { -61.2090812538259f,    21.6681178962575f},
  { -140.111099221292f,    -9.71220758526258f},
  { 124.732911999980f,    -32.2002280863523f},
  { 36.5037140855799f,    -64.4061857506559f},
  { 89.6048695805094f,    24.6486443465280f},
  { -42.2516266863323f,    51.3977519700056f},
  { 62.9279546392183f,    -1.49415933814216f},
  { 51.1101271568500f,    27.7557944695225f},
  { -176.511107945953f,    1.57420154212194f},
  { -31.2708905426501f,    -61.0429234932379f},
  { 29.2311607919843f,    -3.40445792288784f},
  { 80.4260857025137f,    -35.8104351534716f},
  { -39.5237746237144f,    0.881266384690719f}};
  
/* Sphere Covering (43 points) */
const float __SphCovering_43_dirs_deg[43][2] =
{ { 150.212345149448f,    -9.06533823455989f},
  { 123.466675272741f,    -60.1491093328338f},
  { 55.3471500518424f,    -57.5077738972807f},
  { 6.78210142096356f,    -51.9982117393027f},
  { -166.226515523354f,    -54.7518469027015f},
  { -53.0249521081772f,    27.2722180904321f},
  { 28.5963235549794f,    40.5522338659743f},
  { 155.139782187573f,    -35.9645608003618f},
  { -21.9637641185450f,    5.97881459219014f},
  { 90.3153372464717f,    1.82435491547605f},
  { 6.58844168620934f,    -16.7441186049032f},
  { 146.018294089090f,    28.5814266523060f},
  { 34.3883539059569f,    6.97862594469343f},
  { -77.6415108181779f,    57.5249626311347f},
  { -69.2992453210731f,    -32.8448056058744f},
  { 114.832201300120f,    -25.7859655698627f},
  { -22.6685022065559f,    42.0952092082616f},
  { 122.996849880734f,    6.17247432694436f},
  { 65.0765463709589f,    28.9412441476481f},
  { -112.735175769941f,    -52.3815205042453f},
  { -150.521742358819f,    10.3986110238293f},
  { 74.4386767433966f,    63.6785293508397f},
  { -171.314380744116f,    40.1700710166220f},
  { -49.2348362933868f,    -58.6021232859806f},
  { 6.02637008918600f,    18.6984776440944f},
  { 39.3100613661307f,    -26.6551425450762f},
  { 102.633929841784f,    33.5037070702749f},
  { -100.244695836089f,    -88.5964638610792f},
  { -171.629507531438f,    -18.9167745640393f},
  { 0.250182021243874f,    69.9753355193274f},
  { -26.3967385794722f,    -27.4607212050301f},
  { -93.6041149905226f,    28.0422733670879f},
  { 61.3064840789981f,    -6.31972448029298f},
  { -120.934201818263f,    6.29050363274131f},
  { -149.473229593729f,    75.0230936944300f},
  { -140.311634449587f,    -24.3014319226787f},
  { -82.7465647727935f,    2.81688970398118f},
  { -129.878073000255f,    41.4724040849544f},
  { 174.517214818897f,    9.88982450175314f},
  { 82.7637535066474f,    -33.5896507395445f},
  { 140.517899255834f,    57.3874527603033f},
  { -52.7665481425732f,    -5.65354645189437f},
  { -103.241265104623f,    -20.4288101853895f}};
 
/* Sphere Covering (44 points) */
const float __SphCovering_44_dirs_deg[44][2] =
{ { 120.819610259237f,    60.6991488161594f},
  { 29.3950267213918f,    -27.9557567400231f},
  { -0.0728114766052250f,    -17.3073361175168f},
  { 168.919417160469f,    16.7779231148159f},
  { 105.011704691577f,    -18.8084855407595f},
  { -21.8990198876952f,    64.8416336749553f},
  { 49.3156233425002f,    29.5084723648277f},
  { 43.5327603162448f,    -52.1070737203776f},
  { 158.623365581968f,    -64.6124505569029f},
  { 7.35849696286516f,    34.6513415339219f},
  { -53.7915696380622f,    4.27655698285647f},
  { -82.4371675634229f,    53.2948152296838f},
  { 71.6254539693042f,    -24.6675519537673f},
  { 168.031332578017f,    -16.2874712421839f},
  { 45.7862033244943f,    -3.39511871082721f},
  { 136.621786248945f,    -32.6121847410513f},
  { -176.682995284492f,    -42.2871500696304f},
  { -162.055382774802f,    -6.03496445611296f},
  { -76.1231726610812f,    26.2913143451681f},
  { 46.2382670248526f,    59.2209177047219f},
  { 89.1465033444048f,    37.3299192261585f},
  { 17.1085197626064f,    8.66827848253423f},
  { -153.569877828915f,    20.1474879079803f},
  { -69.4424847698558f,    -22.2553996362666f},
  { -170.506510252982f,    82.5746774342542f},
  { 135.246687540631f,    31.5270026770736f},
  { -11.9902877787027f,    -48.5707782088302f},
  { -103.682442606874f,    -30.8543502255900f},
  { 138.145853983993f,    -0.787072123171212f},
  { -20.0162805728953f,    9.25556022254332f},
  { -62.4810475590163f,    -53.3555487559677f},
  { 10.3527744002188f,    -82.5918661681082f},
  { -136.214986214402f,    52.3843852932209f},
  { -115.594235167644f,    25.7498692287695f},
  { 77.5670263048108f,    6.65948845280556f},
  { 97.5231463092174f,    -53.4042501685538f},
  { 109.165648706276f,    12.4738641577932f},
  { -120.825339837188f,    -60.6189347248411f},
  { -36.0384723559337f,    35.2036728484280f},
  { -142.735245922991f,    -31.2473992730497f},
  { -35.1160103057730f,    -22.5292734623391f},
  { 176.877800934836f,    45.8177160032265f},
  { -91.6102218634673f,    -0.511960708261196f},
  { -125.454838821845f,    -2.46772922362846f}};
 
/* Sphere Covering (45 points) */
const float __SphCovering_45_dirs_deg[45][2] =
{ { 77.2175220497810f,    -86.8088355402710f},
  { -140.472062632224f,    -55.6399314851542f},
  { -17.8258629221102f,    14.8424716828640f},
  { -76.2950599996204f,    -16.6656233869703f},
  { 10.2645388997687f,    -1.48757032349816f},
  { -109.933412151751f,    -2.28690374348517f},
  { -44.4305851812148f,    -3.72176194983129f},
  { -163.539343464191f,    27.5873448777540f},
  { 16.8896498848664f,    30.3667631419336f},
  { -4.68564884857987f,    -54.6613195710708f},
  { -12.0298218665668f,    49.5906430841630f},
  { 39.7867622516795f,    0.436387575083440f},
  { 155.684092092947f,    -26.4672123882733f},
  { -74.7308852189133f,    -63.3519434076151f},
  { -167.126059261710f,    -25.1585767841944f},
  { -16.2616881414030f,    -20.7055488004377f},
  { 59.2381064385758f,    -56.8471535594949f},
  { 87.8458891494578f,    35.4953083661496f},
  { 179.221198316922f,    60.8538474208447f},
  { 105.676335733929f,    3.63301078736552f},
  { 143.617600927492f,    3.57141782438896f},
  { 125.775695187118f,    -19.9990918390414f},
  { 125.930393791804f,    27.6102631895592f},
  { -47.2151600655506f,    -37.2926769694750f},
  { 118.682477683399f,    -51.9002359563354f},
  { -71.1040623757352f,    56.0295427858432f},
  { 169.526752423308f,    -56.0524610976484f},
  { 117.702719853725f,    59.4902078684334f},
  { -127.076309382065f,    23.6150284841120f},
  { 176.528296679807f,    2.27853855967626f},
  { -75.7106430485870f,    9.46984643792225f},
  { 90.5502499424753f,    -29.1755838858567f},
  { -129.837965954596f,    54.0952372694815f},
  { -33.7271606103759f,    84.1331226370101f},
  { 55.4863787960592f,    -23.8516600535010f},
  { 76.5700797412832f,    2.61721391237809f},
  { 52.1254083698218f,    26.5353943658938f},
  { -91.5873035516621f,    29.7703140772024f},
  { -48.0207387255046f,    29.7697411194073f},
  { 158.090514832497f,    32.8127199693471f},
  { 21.3902333656190f,    -32.2242923137478f},
  { 47.6826936263774f,    59.5016670243360f},
  { -130.428112483581f,    -25.9773334734364f},
  { -147.221505458865f,    0.0291457900805098f},
  { -94.5036587288780f,    -35.9187241767513f}};
 
/* Sphere Covering (46 points) */
const float __SphCovering_46_dirs_deg[46][2] =
{ { -135.309712898095f,    -6.19367376536420f},
  { 61.9424672315933f,    18.7660866639199f},
  { -15.3758953901308f,    -8.16579449620449f},
  { 114.442589999431f,    41.5102192994330f},
  { -168.186031182702f,    52.7132630676260f},
  { -53.1550135276719f,    -61.1002192727510f},
  { -110.242809361122f,    12.0195086262544f},
  { -178.006527791244f,    20.7794603560096f},
  { 70.3534876641138f,    -61.7476615812488f},
  { 33.0413301296043f,    34.1041668395720f},
  { 21.5323268988115f,    69.6831270438107f},
  { 37.0165113122220f,    -1.84400736784904f},
  { -168.329270631485f,    -8.59150213798669f},
  { 9.66064138370081f,    10.0473878954141f},
  { -146.831894158176f,    20.6310642870707f},
  { -26.5485723951818f,    18.7838483555689f},
  { -57.4046414941572f,    19.6169289896891f},
  { 50.0369772065699f,    -32.5147819158791f},
  { -86.1155566081627f,    35.7325128933338f},
  { 157.019083755602f,    0.0523889689555820f},
  { -95.9761602623642f,    71.5051328323267f},
  { 138.059910314723f,    71.2874088701770f},
  { -110.093840334388f,    -53.0862585922562f},
  { 170.179924309757f,    -30.5100025907163f},
  { 12.9820777220742f,    -25.3917706068127f},
  { -70.9493637710499f,    -31.2817767407576f},
  { -107.257699248490f,    -23.4471518501387f},
  { 10.5235158231678f,    -55.0537956607354f},
  { 129.368140562589f,    11.4081626588498f},
  { -124.022444334018f,    42.5793585451471f},
  { -146.957944873105f,    -34.1041668395720f},
  { 152.446880550458f,    35.9439343197371f},
  { 133.613757824508f,    -23.9353118915901f},
  { -170.454944051420f,    -59.7766867659988f},
  { 71.1900060450048f,    50.7560392394591f},
  { -152.836491851147f,    -88.8313765570828f},
  { 132.525138013759f,    -53.6414546957379f},
  { 93.8848643101367f,    -35.7325128933338f},
  { -46.3883819671768f,    51.2711282972817f},
  { 92.7561374537290f,    18.9924049929965f},
  { -3.99804219864337f,    40.5596823173110f},
  { -48.5759348289863f,    -10.0044160607793f},
  { -27.5541133256364f,    -35.9439343197371f},
  { 104.879924398697f,    -7.55502148659504f},
  { -82.9986662026511f,    -0.293073641787367f},
  { 71.7686934180869f,    -10.5464341349731f}};
 
/* Sphere Covering (47 points) */
const float __SphCovering_47_dirs_deg[47][2] =
{ { 174.528673974800f,    35.0650170620064f},
  { -140.025155552022f,    -38.1836263409035f},
  { 65.1453013063746f,    -19.2874782574889f},
  { 9.07565147487224f,    51.6819390363905f},
  { 160.284943187848f,    -17.6213169892485f},
  { -23.2804211317556f,    -5.61676256144697f},
  { 121.249328605585f,    17.0214301777465f},
  { -45.5014433003143f,    -26.8413538284937f},
  { 7.96124856334279f,    -6.22346757071100f},
  { 5.69978414596143f,    -69.8550143823500f},
  { 91.8909711830814f,    -2.15810283113976f},
  { 93.7244361275001f,    31.6335728269679f},
  { -149.341449300849f,    29.3629410848644f},
  { -169.343405928866f,    63.1972448029298f},
  { -57.6051767224530f,    3.12548477243864f},
  { -133.184039478160f,    -74.2438710930521f},
  { -114.975440748902f,    -15.1266587492489f},
  { 139.205825904985f,    -41.7829472099153f},
  { -88.7511624657645f,    3.81183091522585f},
  { 30.2493067939318f,    81.3542773306256f},
  { -115.153057665393f,    20.0099780371489f},
  { -39.7334771767323f,    23.1744239396564f},
  { -77.6300516622752f,    33.1501921106792f},
  { 27.7741291189667f,    -37.1643344233657f},
  { 29.7101535087137f,    21.4314863268684f},
  { 152.658874934657f,    9.38447572644775f},
  { -35.4064999079044f,    49.8880081798359f},
  { -7.33958935562585f,    -36.1880143404628f},
  { -140.884592244718f,    -1.99670062025141f},
  { -166.679152181508f,    -24.8142291493208f},
  { -120.407080646743f,    45.0109914276824f},
  { 100.330639505358f,    -33.5403763691633f},
  { 38.9066990783586f,    -8.14001139542361f},
  { 113.205001161948f,    -68.5028339858412f},
  { 109.188567018081f,    62.5039658708215f},
  { -50.2982459611496f,    -55.6731630372718f},
  { -4.79915178779529f,    22.0147573623116f},
  { -79.1312010855180f,    -25.3098376421090f},
  { 56.2060137867435f,    46.3923926717428f},
  { 64.0051152940643f,    14.9627928198414f},
  { 138.678704733464f,    43.0743940801402f},
  { 63.9478195145512f,    -49.2096261504010f},
  { -100.198859212478f,    -47.2707369716783f},
  { 124.973554273935f,    -11.3084680024971f},
  { -179.673834975075f,    -50.7491637459175f},
  { -82.5402999665464f,    66.4401859233703f},
  { -173.182223156243f,    5.68740825758661f}};
 
/* Sphere Covering (48 points) */
const float __SphCovering_48_dirs_deg[48][2] =
{ { -104.771062417622f,    -1.27345599545777f},
  { -130.938044921247f,    -15.2882328474758f},
  { -107.538448568104f,    -66.2110028053179f},
  { 172.838448479164f,    56.3968087325221f},
  { 157.935816227811f,    -29.5743625112677f},
  { -13.7234851089735f,    -3.35661594699441f},
  { 85.4280072540058f,    -81.6063787604831f},
  { 122.217627279356f,    -49.0910238868089f},
  { -166.066087340718f,    25.4616714578187f},
  { -138.438062459510f,    49.2399929135430f},
  { -14.7278801238378f,    -35.3446204660302f},
  { -74.0662541765615f,    15.3346424288814f},
  { 86.8260242741250f,    -25.6599148549339f},
  { -87.1640693732521f,    61.7190136914923f},
  { 50.6804088105018f,    -21.2807984267490f},
  { 11.1274133392357f,    12.4119847159190f},
  { 72.8974202744947f,    -51.2344589983933f},
  { -166.209326789501f,    84.8264015691184f},
  { -19.4507712291012f,    29.8545388730867f},
  { -168.535535437732f,    -27.7323031999221f},
  { -98.2966393326440f,    -32.9972123793792f},
  { -19.1677300783066f,    -63.5352899020570f},
  { 16.0496937572046f,    -20.4780845557708f},
  { -55.0268666443643f,    41.7084626965483f},
  { -156.148187907003f,    -2.21476835707820f},
  { -130.216118099382f,    19.1534061334283f},
  { 63.1113011336602f,    62.6815827873121f},
  { -9.75403350430713f,    61.4898305734399f},
  { 38.8161717467279f,    5.69479941314379f},
  { -61.4325347939269f,    -45.4172185044301f},
  { 170.701315903326f,    0.342972536165311f},
  { -44.2695840407831f,    -20.8533719115814f},
  { 73.1896287500114f,    2.30867613970014f},
  { 28.7218013121130f,    -49.7155478835015f},
  { -73.0750371909852f,    -12.3770342904160f},
  { 126.554917788496f,    24.7271395644609f},
  { 21.1994384198405f,    39.0350416244679f},
  { -139.045397722348f,    -42.5461269930295f},
  { 122.085846986476f,    54.1863375589073f},
  { 139.807431589872f,    -1.07309265450052f},
  { 53.7571921703544f,    29.9920487439181f},
  { 103.968921504439f,    4.55850951384034f},
  { -43.4479625625655f,    8.76453539211620f},
  { 173.835395042692f,    -60.0173290399537f},
  { 158.038948630935f,    28.6725269417318f},
  { -98.6862506333330f,    31.5630990181668f},
  { 120.493024316012f,    -21.4303404112782f},
  { 88.0808018454615f,    32.9347599797100f}};
 
/* Sphere Covering (49 points) */
const float __SphCovering_49_dirs_deg[49][2] =
{ { -93.1285600205640f,    -56.4999411356456f},
  { 91.5815739737108f,    -34.3619978473809f},
  { -111.434561574994f,    -29.1360497979926f},
  { -1.53902193350090f,    -19.4358743264278f},
  { 7.26338596887345f,    -43.9550302112562f},
  { -139.962130194558f,    53.5726997603222f},
  { -152.670334090559f,    -77.7675615331066f},
  { 74.8454767779394f,    69.7232340894699f},
  { -173.600482346688f,    35.8511151569259f},
  { 24.1232420483931f,    34.9687601524244f},
  { 161.281889751375f,    -53.1338140892520f},
  { -112.569018009353f,    30.4320803305785f},
  { 130.657295601633f,    -30.4836465321403f},
  { -82.5460295444977f,    48.5919776472500f},
  { -48.9403359866895f,    26.8023926984248f},
  { 104.702307482207f,    43.9132042922117f},
  { 44.5302798375676f,    9.90815915119733f},
  { 144.414012262724f,    32.9427813888418f},
  { 112.947170154139f,    19.2863323418986f},
  { 14.6808975846371f,    60.1662980666877f},
  { 11.6866201472834f,    5.10786144781178f},
  { 63.0081687305366f,    39.2814134763741f},
  { 102.330262210365f,    -8.59207509578183f},
  { -35.8035596599300f,    -61.2606474553876f},
  { -85.1816354020995f,    -11.0156865691852f},
  { -69.2247608077061f,    -34.6513415339219f},
  { 52.7751425095001f,    -42.5570131911370f},
  { -145.250530643615f,    -46.2491532229601f},
  { 105.361208946607f,    -59.3928050432611f},
  { 155.168430077330f,    61.0601122270918f},
  { -169.331946772964f,    2.42149152956140f},
  { 162.124137710218f,    -19.4020698165151f},
  { -138.776107558637f,    -12.5896016324096f},
  { -11.2981547621847f,    28.2021285919294f},
  { -32.6477081243494f,    55.7596796643366f},
  { 162.645529303787f,    10.8649986690658f},
  { -143.577493881833f,    18.9316714667127f},
  { -32.7869368685662f,    -30.3679090575239f},
  { -168.982442517934f,    -27.5231736046994f},
  { -103.201158058964f,    78.9020179674657f},
  { 34.9487066295948f,    -18.6234201729323f},
  { 133.098095808890f,    -0.836862155568080f},
  { -52.3820934620404f,    -4.85879669426841f},
  { 78.9478545910761f,    15.5999218880269f},
  { -112.861226484870f,    4.61116433521287f},
  { -79.1884968650311f,    16.6215056367452f},
  { 40.2376800364475f,    -72.6796963123449f},
  { -23.5714836916821f,    2.85533517203446f},
  { 68.8637973967736f,    -11.7983469173339f}};
 
/* Sphere Covering (50 points) */
const float __SphCovering_50_dirs_deg[50][2] =
{ { -79.0051503705892f,    0.825402999665464f},
  { -111.990330636271f,    -45.5088917516510f},
  { -141.211178187943f,    13.7257769401540f},
  { -124.904799338519f,    41.8408159472235f},
  { -130.817723784270f,    73.1838991720601f},
  { -69.2419495415600f,    -59.0604895220853f},
  { -36.9019197531958f,    -37.5218600875274f},
  { -75.8424233414671f,    55.4903895006251f},
  { 172.517592113891f,    -30.9546178397379f},
  { -16.0451100948436f,    -13.0943774499198f},
  { -57.5478809429399f,    23.3846994504694f},
  { 34.9000052170087f,    15.9179134643245f},
  { 132.015205576093f,    7.18259891976000f},
  { 19.8484039389220f,    -14.9776897225148f},
  { -90.4070104936926f,    28.6690891949610f},
  { 157.844142980591f,    27.7775668657374f},
  { 139.647003407236f,    -23.9009344238823f},
  { 64.1311660089930f,    18.1736483037546f},
  { -4.67126760792209f,    -67.2996226160665f},
  { -163.705501224779f,    -12.3214573842884f},
  { 123.134359751565f,    38.1200280256439f},
  { -162.983574402914f,    42.3937202195247f},
  { -135.143555137507f,    -17.1715451200708f},
  { -47.9852153422064f,    -7.18259891976000f},
  { 1.34977397376919f,    -38.7159041325800f},
  { 5.02277721523485f,    37.9406922357680f},
  { -112.981547621847f,    9.20284810539129f},
  { -147.439229421015f,    -76.5987276310398f},
  { 100.370746551018f,    14.9129454916651f},
  { -25.8054461348971f,    16.0468289682290f},
  { 42.1857365398923f,    -43.4748915789366f},
  { 157.975923273471f,    57.6739316578687f},
  { 79.2572518004468f,    -6.43718082829480f},
  { 77.0685530230470f,    -35.1492418578906f},
  { -173.027524551557f,    14.9404474658313f},
  { 41.3841685845042f,    46.9252434212144f},
  { -102.794358024421f,    -17.7634105224409f},
  { 162.508019432955f,    -2.59057137490450f},
  { -72.5536455974162f,    -29.2472036102480f},
  { 154.767359620738f,    -56.9669017386772f},
  { 4.04697279434754f,    9.17133542665909f},
  { 48.5902587738646f,    -12.4916258494422f},
  { 77.2232516277324f,    -69.4367551919045f},
  { -152.274993211919f,    -45.1937649643291f},
  { 0.197985566107456f,    72.1411159849220f},
  { 108.523935975729f,    -14.7072536432131f},
  { 112.901333530529f,    -44.3727164439066f},
  { 84.1617705267667f,    41.3045274509811f},
  { 94.9333770752261f,    69.5341580170767f},
  { -32.5892664292461f,    45.3965920238054f}};
 
/* Sphere Covering (51 points) */
const float __SphCovering_51_dirs_deg[51][2] =
{ { -101.568228342841f,    -23.6368008803270f},
  { -94.4578221052675f,    5.01928217268455f},
  { -34.5293015235591f,    -12.7139334739530f},
  { 153.231832729787f,    61.0658418050432f},
  { 65.5463717629662f,    -66.8584451138158f},
  { -85.2102832918560f,    60.4241290744966f},
  { 135.556084750001f,    -22.5779748749252f},
  { 0.178275817954956f,    67.7866367419277f},
  { -36.3702149193144f,    20.7874817651414f},
  { -40.9704930564198f,    47.1509887924960f},
  { 103.722549652533f,    -21.4165894241950f},
  { -110.494910790979f,    32.4431621914877f},
  { -74.1350091119772f,    30.6698578155578f},
  { -4.34771834101171f,    -55.3935596332480f},
  { 99.1961830709994f,    11.8739773462912f},
  { -5.23494348677179f,    -26.6597262074372f},
  { 15.8961410681096f,    -12.5993419149268f},
  { -69.4367551919045f,    -17.8671158833596f},
  { 53.2833560737812f,    16.2296025048757f},
  { -43.5659918683624f,    -39.6567008321848f},
  { -82.1277703540522f,    -49.5362120936256f},
  { 117.702719853725f,    39.3054777037696f},
  { 172.162358280910f,    -73.6881020317752f},
  { -163.419022327213f,    -41.7468508688220f},
  { 156.669579500572f,    -0.651453013063746f},
  { 71.3561638055927f,    -34.4897674356950f},
  { 22.9177388474378f,    14.8023646372048f},
  { -177.932043277877f,    11.8075142420560f},
  { -60.7220671279647f,    5.83442922781717f},
  { 82.4543562972768f,    60.7621741736238f},
  { 123.965148554505f,    5.76567429240147f},
  { 76.1289022390325f,    -3.92579222067737f},
  { -52.0549345610207f,    -74.7308852189133f},
  { -124.286004919778f,    2.29853478672632f},
  { -141.927375431856f,    52.3626128970059f},
  { -156.681038656475f,    -8.35487056859767f},
  { 33.7861752632744f,    -40.8644958643206f},
  { 110.930358715279f,    -50.7697902265422f},
  { -144.889567232683f,    21.1346941889907f},
  { 37.7040606663790f,    45.1714196103190f},
  { 173.812476730887f,    -20.6769009106811f},
  { -1.48264288646003f,    34.9601657854974f},
  { -169.669991872091f,    83.8695620512499f},
  { -124.515188037831f,    -54.7999753574925f},
  { 148.075212573610f,    26.9427673582318f},
  { 155.197077967086f,    -44.9949486094187f},
  { 46.1190918034654f,    -11.4625936493872f},
  { -10.0365016973066f,    5.70923794958109f},
  { -131.912073172969f,    -26.5565938043137f},
  { -178.407598247836f,    38.3394708611790f},
  { 77.4123277001255f,    31.2961006856358f}};
 
/* Sphere Covering (52 points) */
const float __SphCovering_52_dirs_deg[52][2] =
{ { -129.832236376645f,    -2.67645774839461f},
  { 174.139062674111f,    -34.9996998733615f},
  { 39.7764490113671f,    17.6035552975994f},
  { -104.547608877521f,    21.1026085524634f},
  { -63.7816617539632f,    70.1013862342562f},
  { -18.4916398800522f,    -5.37159392091049f},
  { -155.139782187573f,    -18.3850697301579f},
  { 12.0561779251428f,    37.5063902270588f},
  { 106.724848499018f,    -36.7833174896037f},
  { 170.775800416693f,    25.8449802227612f},
  { 173.228059779853f,    -6.85887776551108f},
  { 54.4309905374282f,    44.3589654568235f},
  { 61.9539263874959f,    -2.50881029753934f},
  { 31.5052302808586f,    -47.5342975574385f},
  { -12.9133227866585f,    18.8892725898730f},
  { -125.334517684868f,    -34.8851083143353f},
  { 132.737132397958f,    26.0907791168723f},
  { -98.0617266366404f,    -63.2602701603942f},
  { -71.3160567599336f,    38.0982556294290f},
  { -53.9193392263764f,    -47.2632885203416f},
  { 38.0443975966867f,    -16.4851416815040f},
  { 142.826919170212f,    -55.8353100932939f},
  { 7.92801701122520f,    -20.8986355773968f},
  { -156.400289336861f,    -51.9621153982095f},
  { -32.9805966033205f,    42.5587320645224f},
  { -9.22462050160626f,    -68.9382819101407f},
  { 172.001930098273f,    -80.2885758316823f},
  { -111.572071445825f,    49.4943861745810f},
  { 75.7163726265383f,    21.1679257411083f},
  { 88.4646835681991f,    74.2438710930521f},
  { 142.454496603377f,    -25.6490286568264f},
  { -161.597016538697f,    43.4009800233647f},
  { 10.6644634407700f,    62.2977010645744f},
  { 148.871623908842f,    51.2493559010668f},
  { -102.994893252717f,    -9.25957092710923f},
  { 100.038431029842f,    47.0885363928267f},
  { -135.917048160934f,    25.6381424587190f},
  { 120.435728536499f,    -6.84340790504255f},
  { -67.3798367073848f,    -14.0065262597681f},
  { 15.2074457983623f,    4.39813862698323f},
  { -77.0570938671444f,    8.25116520767899f},
  { 79.7901025499184f,    -63.4035096091769f},
  { 148.040835105902f,    3.49286531067652f},
  { -158.674931783530f,    70.8806088356342f},
  { -13.6530113001724f,    -38.9261796433930f},
  { 104.123620109125f,    16.0353698123264f},
  { -161.849117968555f,    9.71048871187719f},
  { 89.8455118544644f,    -10.4914301866405f},
  { -41.8230542555744f,    -17.9731130754588f},
  { -46.7327296020505f,    13.7418197584177f},
  { 67.5517240459241f,    -34.0554654269859f},
  { -88.1151793131693f,    -34.2628761488232f}};
 
/* Sphere Covering (53 points) */
const float __SphCovering_53_dirs_deg[53][2] =
{ { -71.9921469581879f,    24.6308826548790f},
  { 151.398367785369f,    35.7955382507982f},
  { 134.347143802275f,    62.2232165512074f},
  { -39.2143774143438f,    38.1160173210780f},
  { 76.0143106800063f,    31.7876984738581f},
  { -139.629814673382f,    85.4967621894215f},
  { -179.261305362581f,    -10.0313450771505f},
  { 1.07504071100396f,    -8.71468806393982f},
  { 146.448012435438f,    -16.1402210888353f},
  { -66.1594366037562f,    56.7256865069272f},
  { 39.4469982791669f,    41.3509370323866f},
  { -125.460568399796f,    -50.9204781266617f},
  { -98.6117661199660f,    3.57456909226218f},
  { 32.3446134507252f,    -12.9752022285326f},
  { -124.486540148074f,    -18.9471413271812f},
  { 109.033868413396f,    37.6381705199389f},
  { -81.9272351257564f,    -76.5471614294780f},
  { -141.383065526482f,    30.0441879032750f},
  { -125.225655703793f,    11.0231350205219f},
  { -154.349100430292f,    -30.6119890782496f},
  { 167.710476212743f,    -37.0600561046519f},
  { -126.440326229470f,    57.4218302280111f},
  { 128.955610950094f,    -46.3889549249720f},
  { 18.1472922451786f,    15.5930463944854f},
  { 99.6774676189093f,    7.38829076821197f},
  { -57.2877581039505f,    -24.1902781104234f},
  { -1.98879380267860f,    64.4004561727045f},
  { -101.258831133470f,    34.8089049275829f},
  { 70.8347722120237f,    61.8794418741289f},
  { -175.439676869058f,    51.9283108882968f},
  { -29.5892594139411f,    -19.1281959904425f},
  { 77.9108009818893f,    1.19381486193458f},
  { -45.0264612881509f,    7.69768797758261f},
  { -72.5651047533188f,    -6.26414757416529f},
  { 61.2606474553876f,    -18.9746433013475f},
  { 130.628647711876f,    14.7359015329696f},
  { 49.2892672839242f,    12.1547266659053f},
  { 158.915574057485f,    8.91063962987456f},
  { 3.13912116796275f,    -34.5333122281250f},
  { -75.3668683715085f,    -47.7531674351785f},
  { 79.3374658917651f,    -48.6687539917975f},
  { -175.714696610721f,    -60.8653065767474f},
  { -172.918662570482f,    22.4192655656740f},
  { 95.7985433458736f,    -26.6860822660132f},
  { 38.4918776346838f,    -41.2500964604436f},
  { -16.9727287651604f,    11.5995305624235f},
  { -1.35899859427080f,    37.1528752674631f},
  { 111.256944658503f,    -72.5421864415135f},
  { -96.3600419851018f,    -26.6757690257009f},
  { 20.7250293654721f,    -66.6865577752765f},
  { -152.326559413481f,    -0.706227778278253f},
  { -29.1475089538952f,    -50.1842273599185f},
  { 120.819610259237f,    -14.6167263115824f}};
 
/* Sphere Covering (54 points) */
const float __SphCovering_54_dirs_deg[54][2] =
{ { 43.8031963955466f,    0.662912168966363f},
  { -111.703851738705f,    24.7563604120126f},
  { 120.034658079907f,    16.0032841757990f},
  { -14.6877730781787f,    30.6074054158886f},
  { 42.1158356888863f,    -32.4993120554106f},
  { 43.6479248330661f,    30.8497665632289f},
  { 67.5689127797780f,    50.6689496545992f},
  { 99.5514169039805f,    -19.4862946123993f},
  { 108.426533150557f,    -68.5601297653543f},
  { -49.9011862091239f,    28.8925427350620f},
  { 18.2624567619999f,    -16.1253241861619f},
  { -35.2231534134625f,    57.6166358783556f},
  { 67.4256733309953f,    -12.9568675790884f},
  { -172.637913250868f,    -28.2565595824668f},
  { 176.132955801166f,    28.4983477720120f},
  { 99.7863295999842f,    38.2082635260941f},
  { 79.3431954697164f,    -41.5211054975405f},
  { -173.629130236445f,    54.5558953367667f},
  { -76.6732121444068f,    -28.5516328469592f},
  { -149.209669007969f,    -76.3294374673283f},
  { -67.0131437185011f,    0.823225760043967f},
  { 151.553066390054f,    -22.7578836225963f},
  { -117.771474789141f,    79.9505307325551f},
  { -43.5144256668006f,    -48.8257444276634f},
  { -124.154224626898f,    49.5385039248061f},
  { 166.965631079073f,    -50.7972922007085f},
  { 123.523971052254f,    -42.4567455769891f},
  { -145.680248989963f,    -18.2126094338235f},
  { 127.013284024601f,    65.1854083520338f},
  { 71.7056680606225f,    18.0361384329232f},
  { -114.201947725476f,    -26.5313836613279f},
  { -36.1307185609497f,    4.92520250272407f},
  { -44.6299744939203f,    -20.3818276461888f},
  { 150.670711385553f,    9.70533209172102f},
  { -8.81209088911206f,    0.517850714395141f},
  { -81.8584801903407f,    51.2321671672128f},
  { 95.0021320106418f,    5.69783608945799f},
  { 3.11912494091269f,    -44.6792488643016f},
  { 41.8780582039070f,    -62.6873123652634f},
  { -16.1052706633323f,    -24.0630814799043f},
  { 15.8193647235620f,    14.1744028937414f},
  { -83.6346493552463f,    23.6322172179659f},
  { -93.5754671007661f,    -52.5889312260826f},
  { 141.795595138976f,    39.4693436331770f},
  { 175.651671253257f,    -2.97674492882268f},
  { -159.849495263548f,    4.44357418013710f},
  { 34.0354119041563f,    71.3160567599336f},
  { 126.394489605860f,    -9.89039745954827f},
  { 14.8504930919958f,    45.2699683510815f},
  { -96.8642448448170f,    -5.07995840318891f},
  { -148.258559068052f,    27.8480406745385f},
  { -141.938834587759f,    -48.5547353905665f},
  { -126.978906556893f,    3.47309826674451f},
  { -29.7101535087137f,    -74.0032288190971f}};
 
/* Sphere Covering (55 points) */
const float __SphCovering_55_dirs_deg[55][2] =
{ { -40.5826006291162f,    -58.9401683851078f},
  { -100.124374699111f,    42.8681292738931f},
  { -177.582539022847f,    -4.38467411879765f},
  { 18.7271255338510f,    12.8869667280825f},
  { 58.7682810465685f,    -36.7225839633199f},
  { 6.08194699531369f,    -11.3353970188682f},
  { -138.059910314723f,    46.6112625494827f},
  { -49.0663867016183f,    -27.4802017700645f},
  { 154.773089198689f,    -6.88752565526763f},
  { 147.164209679352f,    -29.8642791556039f},
  { -121.489970879540f,    74.8683950897447f},
  { 114.751987208801f,    -40.3625848357860f},
  { 53.7749538620034f,    51.8320539787148f},
  { -123.403649915277f,    -7.56189698013661f},
  { -11.2150758818907f,    16.7343783223860f},
  { 139.561059737966f,    42.1662559748578f},
  { -154.922058225423f,    -56.3458154887554f},
  { -126.325734670444f,    21.7511967765514f},
  { -69.2133016518035f,    -4.49903649470576f},
  { -14.7043888542374f,    46.8925848268920f},
  { -42.4636210705307f,    28.5837184834865f},
  { 23.8625462516085f,    -61.9940334331551f},
  { -150.567578982429f,    3.81354978861125f},
  { 84.0299902338865f,    -59.9600332604407f},
  { 47.4787206513108f,    20.9948924869788f},
  { -151.295235382245f,    -25.2640010184985f},
  { 89.6564357820712f,    -26.8127059387371f},
  { -163.166920897356f,    26.1303132047363f},
  { 65.1510308843259f,    -6.04871544319610f},
  { 7.96067560554766f,    72.1010089392628f},
  { -21.9110520013929f,    -10.8844792341003f},
  { 97.9012984540038f,    46.4812011299880f},
  { 138.334930056386f,    13.4943019909211f},
  { 23.1658295727294f,    -34.4078344709913f},
  { -63.0826532439036f,    56.3309185860820f},
  { -70.8462313679263f,    24.2974212181128f},
  { 146.407905389779f,    -89.5017371773859f},
  { -43.0852802782476f,    4.52653846887204f},
  { 121.025875065484f,    -10.5790927292955f},
  { 17.7393462950454f,    39.0940562773663f},
  { -97.8096252067828f,    11.7399052222306f},
  { 39.1215582515326f,    -9.54547686687952f},
  { 177.164279832402f,    -32.8046985602153f},
  { 115.857795753404f,    72.8172061831763f},
  { 110.552206570492f,    20.6350749916366f},
  { -13.7504141253446f,    -38.6351170834665f},
  { 175.760533234331f,    54.1078423409744f},
  { 93.3520135606650f,    -0.832794155222652f},
  { 168.965253784080f,    22.5183872642316f},
  { -77.2404403615863f,    -37.2445485146840f},
  { 75.4929190864373f,    23.9221338623021f},
  { -102.376098833975f,    -61.0371939152866f},
  { -94.9276474972748f,    -17.2070685033689f},
  { -120.017469346054f,    -36.8520724250194f},
  { 152.263534056016f,    -61.0486530711892f}};
 
/* Sphere Covering (56 points) */
const float __SphCovering_56_dirs_deg[56][2] =
{ { -108.896358542564f,    38.6947046941601f},
  { 95.0307799003983f,    31.1803632110194f},
  { -24.8337097143553f,    -67.2537859924560f},
  { -14.5565657430937f,    34.3270474218779f},
  { 64.6582871805134f,    -14.3136316379582f},
  { -90.7851626384789f,    60.8824953106013f},
  { 127.053391070260f,    -40.7653741657629f},
  { -141.812783872830f,    -29.1566762786173f},
  { 117.823040990702f,    12.4841773981055f},
  { -156.171106218809f,    -2.67078546622282f},
  { -71.0066595505629f,    -30.6435017569818f},
  { 18.1753671771400f,    46.6530884685273f},
  { 3.76828612279591f,    -42.2768368293181f},
  { 155.305939948161f,    -22.3528024614388f},
  { -41.4792795784960f,    -42.6716047501632f},
  { 146.138615226068f,    3.65518425403709f},
  { 69.5971833745411f,    -41.5027708480963f},
  { 122.423892085603f,    -14.2168017705811f},
  { -165.682205617980f,    26.3251188550808f},
  { -95.4375799349412f,    -13.7469763785738f},
  { 53.4861831332575f,    70.6800736073384f},
  { -134.857076239942f,    18.7357199007779f},
  { -109.394831824328f,    -36.7592532622082f},
  { -24.3776353094311f,    65.9875492652169f},
  { -87.2500130425218f,    -58.8771430276434f},
  { -173.073361175168f,    -30.7265806372758f},
  { 164.244081552202f,    25.2250398884296f},
  { -146.453742013390f,    -57.9947880231419f},
  { -44.2581248848804f,    16.8781907289638f},
  { 178.333113734469f,    -83.4971394844149f},
  { -101.992217111238f,    12.5489216289553f},
  { 11.2082003883492f,    15.3197455262080f},
  { 104.232482090199f,    -61.4611826836834f},
  { 133.487707109579f,    34.4571088413726f},
  { 170.265867979027f,    53.8929831678004f},
  { 34.7911432359338f,    -30.3186346871426f},
  { -70.7946651663645f,    1.57362858432681f},
  { 66.3198647863928f,    45.2722601822620f},
  { -76.3695445129874f,    28.4702728400506f},
  { 40.8707984000670f,    -62.2690531748179f},
  { -51.7317863645669f,    43.6651135669200f},
  { -161.900684170117f,    79.1483898193719f},
  { 41.1160243363830f,    25.7487233131792f},
  { 39.2424523463052f,    -1.23672940078988f},
  { -17.9593620883757f,    5.10958032119717f},
  { 68.9554706439946f,    13.1637053431307f},
  { -46.7602315762167f,    -10.8162972564797f},
  { -18.7431683521146f,    -21.9253759462712f},
  { 177.582539022847f,    -1.62473641965248f},
  { -124.452162680366f,    -6.79069578789052f},
  { 163.608098399607f,    -53.4907667956185f},
  { 10.2009405845092f,    -10.9096893770860f},
  { -144.631736224874f,    49.5213151909522f},
  { 115.691637992816f,    57.9947880231419f},
  { 95.4032024672334f,    -28.1534271793433f},
  { 92.1029655672798f,    -0.917534613122500f}};
 
/* Sphere Covering (57 points) */
const float __SphCovering_57_dirs_deg[57][2] =
{ { 157.425883790145f,    -74.1407386899285f},
  { 128.835289813117f,    5.11049705366938f},
  { -177.238764345769f,    -20.7112783783890f},
  { 131.728726678528f,    -24.2618978348147f},
  { 95.4089320451847f,    -30.2275343977168f},
  { -81.8928576580486f,    70.1987890594285f},
  { -52.7287329280945f,    -56.3022706963255f},
  { 31.4124111180474f,    -48.2229928271857f},
  { -110.168324847755f,    -65.3057294890112f},
  { -38.2752995881244f,    2.48892866204830f},
  { 153.741765167454f,    17.2546240003647f},
  { 77.5612967268595f,    -2.51551390374237f},
  { 73.9745809293406f,    -59.4902078684334f},
  { 139.853268213483f,    60.5444502114741f},
  { 52.3018793707221f,    -0.612319995656311f},
  { 104.868465242795f,    -7.94463278728400f},
  { -20.4500096238093f,    -18.9832376682744f},
  { 156.377371025056f,    -11.4998359060708f},
  { 8.49295339722419f,    -21.9185004527296f},
  { -118.699666417253f,    -38.5193796088501f},
  { 4.17382565018951f,    -77.8535052023763f},
  { -64.3603491270454f,    -12.4475080992171f},
  { -23.1830183065834f,    28.3923505799128f},
  { -87.1869876850574f,    39.9769842396629f},
  { -147.719978740629f,    -23.7645704686412f},
  { 125.626726160384f,    34.4685679972752f},
  { 120.338325711327f,    -50.4655496373278f},
  { -122.985390724831f,    45.9420478447699f},
  { -159.150486753489f,    64.1197068530904f},
  { 66.0047379990708f,    -30.3501473658748f},
  { -49.9183749429779f,    46.0841413779624f},
  { -7.33443273546967f,    58.8656838717408f},
  { 90.2580414669586f,    50.9663147502721f},
  { 161.081354523080f,    -42.6160278440355f},
  { -179.095147601993f,    8.86480300626410f},
  { -82.4199788295689f,    -37.2869473915237f},
  { -80.5521364174424f,    10.1298938179130f},
  { 99.9009211590103f,    20.5107431500932f},
  { 65.4145914700861f,    81.5891900266292f},
  { -57.6166358783556f,    19.3264393875578f},
  { -44.1773378357670f,    -29.4775326438906f},
  { 45.5879599273791f,    52.5728884078189f},
  { -107.796279575913f,    16.5114977400801f},
  { 166.323918348527f,    38.5657891902557f},
  { -162.393427873929f,    34.5545116665448f},
  { -123.621373877426f,    -8.49868297517550f},
  { 9.58844870151433f,    34.0440062710833f},
  { -6.64401859233703f,    6.48244449411013f},
  { 20.1050890311406f,    5.30879774656416f},
  { -8.91006667207943f,    -47.9244818159226f},
  { 40.8043352958318f,    24.5266043361652f},
  { 71.2014652009074f,    26.4723690084294f},
  { 37.5923338963284f,    -19.7859515392527f},
  { -154.326182118487f,    2.97193208334358f},
  { -136.300929883672f,    19.2399227604930f},
  { -96.9845659817945f,    -13.6982749659877f},
  { -160.462560104338f,    -50.2495445485635f}};
 
/* Sphere Covering (58 points) */
const float __SphCovering_58_dirs_deg[58][2] =
{ { -96.0219968859747f,    47.0398349802406f},
  { 90.9112133534077f,    -40.3161752543804f},
  { 82.3684126280071f,    15.3461015847840f},
  { -25.9091514958158f,    -0.125214196547890f},
  { 128.342546109304f,    50.6872843040434f},
  { 56.5182757850898f,    -1.28737886987945f},
  { 55.1752627133032f,    26.3577774494033f},
  { 141.297121857212f,    -5.37560462547641f},
  { 29.7892216844418f,    5.28129577239788f},
  { -9.87721943026026f,    -72.7599104036632f},
  { -81.8298323005842f,    -10.5235158231678f},
  { -37.0480239909542f,    -50.1641738370890f},
  { 45.8555312177052f,    -52.6003903819852f},
  { 86.4650608631926f,    -10.1906273441968f},
  { -163.590909665753f,    0.573015090910336f},
  { 169.836149632679f,    -18.2171930961845f},
  { -112.116381351200f,    23.5078853764225f},
  { -49.6926295716963f,    54.4401578621503f},
  { 115.531209810179f,    -24.6457795575524f},
  { 40.2222101759789f,    56.7004763639414f},
  { -7.31036850807417f,    43.0044932291342f},
  { 130.307791346603f,    -54.4401578621503f},
  { -165.114977400801f,    -75.1262260975535f},
  { 108.415073994654f,    74.8798542456473f},
  { -0.689669297998972f,    13.1654242165161f},
  { -162.347591250319f,    -27.2258085090265f},
  { 8.26949985712317f,    -43.4565569294924f},
  { -109.967789619459f,    -4.23702289499244f},
  { -106.999868240681f,    -31.7109221293105f},
  { -51.0224646141949f,    -20.4110484937404f},
  { 108.598420489096f,    28.1706159131972f},
  { -55.2932920191001f,    4.78316626531114f},
  { 81.9788013273182f,    -69.6258312642976f},
  { 112.328375735398f,    1.58892655745680f},
  { -84.4711677361373f,    15.7374317588583f},
  { -176.173062846826f,    59.8970079029763f},
  { 163.430481483116f,    36.4922549296773f},
  { -114.379564641966f,    71.4134595851058f},
  { 23.8533789268864f,    32.0529779330036f},
  { -165.481670389684f,    28.1282170363575f},
  { 138.890699117663f,    20.0563876185545f},
  { -20.3228129932903f,    -26.3996033684478f},
  { 4.62451425183941f,    -12.1495700457491f},
  { -64.0624110735774f,    30.3535851126456f},
  { 168.741800243979f,    8.15147055132622f},
  { 148.063753417707f,    -31.4897604203900f},
  { -138.036992002918f,    11.6407835236729f},
  { 80.5234885276859f,    46.7734096055048f},
  { -74.3126260284678f,    -38.4758348164202f},
  { -92.4295515105044f,    -62.9566025289749f},
  { 31.5671097227327f,    -22.3390514743557f},
  { -139.005290676689f,    42.6962419353538f},
  { -31.0233727751536f,    25.8272185311121f},
  { 179.249846206678f,    -50.0747924210486f},
  { -134.473194517204f,    -46.7980467906954f},
  { 61.7362024253462f,    -28.1700429554021f},
  { -135.579003061807f,    -15.7448802101950f},
  { -3.80472623856623f,    72.6453188446371f}};
 
/* Sphere Covering (59 points) */
const float __SphCovering_59_dirs_deg[59][2] =
{ { 87.7828637919934f,    -7.58366937635158f},
  { 108.054110583722f,    4.74827313558767f},
  { -99.3737999874900f,    13.4232552243249f},
  { -103.401693287260f,    -13.3384574706456f},
  { 179.605080039659f,    36.7770149538573f},
  { 92.0284810539128f,    -34.0451521866735f},
  { 32.5938500916071f,    -42.6933771463782f},
  { 13.3923155033879f,    5.88943317614973f},
  { 165.882740846276f,    -46.5694366304382f},
  { -5.10534043351320f,    24.0097964049571f},
  { 118.384539629931f,    -22.1327866681086f},
  { -179.192550427165f,    10.5922707585835f},
  { -87.6224356093568f,    -68.3080283354967f},
  { 178.883153217794f,    -19.7704816787842f},
  { 133.012152139621f,    80.0364744018247f},
  { 146.889189937689f,    55.3551714609742f},
  { -68.2965691795941f,    17.2569158315453f},
  { 61.6617179119792f,    -27.0166789138037f},
  { 24.2223637469507f,    36.8102465059749f},
  { 8.31590943852877f,    -19.4192585503690f},
  { -9.59016757489972f,    49.9057698714850f},
  { 87.2041764189113f,    23.3084960637170f},
  { 9.66751687724238f,    -72.9833639437643f},
  { 119.645046779219f,    32.6563024912764f},
  { -16.3791444894048f,    -0.596792839408265f},
  { -32.8940799762557f,    72.3932174147795f},
  { -149.541984529145f,    26.4580450635512f},
  { 44.8093102837963f,    61.2434587215337f},
  { -156.153917484955f,    -1.24515188037831f},
  { -47.0667639966117f,    -51.5404184609932f},
  { -54.6194936520262f,    -24.8382933767163f},
  { 61.0601122270918f,    33.5512625672708f},
  { -126.784100906549f,    8.93183906829440f},
  { 122.641616047753f,    -52.7293058858897f},
  { -45.1909001753534f,    0.552457365221042f},
  { 94.0109150250655f,    52.8410326559402f},
  { 144.975510901952f,    -26.5159138008594f},
  { -76.4898656499649f,    -7.36938316097265f},
  { -131.241712552666f,    -17.4333868324456f},
  { -4.95362120936256f,    -46.6851741050546f},
  { -156.451855538423f,    -32.0208922964763f},
  { 132.851723956984f,    3.49395393048727f},
  { -35.9376317839906f,    24.9557497247181f},
  { 68.8466086629197f,    -58.0234359128985f},
  { 143.279555828365f,    -77.5326488371030f},
  { -24.4887891216865f,    -24.6005158917370f},
  { -85.2274720257100f,    -37.3608589470956f},
  { 39.0401982446240f,    12.7740940424417f},
  { 37.8180792676100f,    -15.2744818603926f},
  { 64.3259716593375f,    2.54227103277498f},
  { 158.474396555234f,    -1.68352188943290f},
  { -118.080871998511f,    -42.6515512273336f},
  { -101.270290289373f,    65.9302534857038f},
  { -53.0811019721000f,    45.2762708868279f},
  { -153.558418673012f,    -59.2667543283324f},
  { -122.635886469801f,    37.0010414517534f},
  { -88.1438272029258f,    40.2371070786523f},
  { 150.258181773058f,    25.3562472235146f},
  { -154.790277932543f,    57.9489513995315f}};
 
/* Sphere Covering (60 points) */
const float __SphCovering_60_dirs_deg[60][2] =
{ { 165.665016884126f,    9.90071069986063f},
  { 107.733254218449f,    -51.8400753878466f},
  { 155.649714625239f,    67.2480564145047f},
  { -172.357163931254f,    -38.5434438362456f},
  { -123.827638683674f,    65.1682196181798f},
  { -50.2827761006811f,    -44.4758488470302f},
  { 166.100464808426f,    -17.9318601142094f},
  { 20.8866034636990f,    -52.2680748608094f},
  { 65.1109238386668f,    -17.2145169547056f},
  { -145.038536259417f,    -24.1834026168818f},
  { -14.2534710694695f,    17.7106984052889f},
  { 161.900684170117f,    -63.8103096437198f},
  { 58.4646134151492f,    8.54165480981031f},
  { -88.3672807430269f,    -54.3301499654852f},
  { 11.3755040645274f,    5.55345072508502f},
  { 110.844415046009f,    1.88938562522340f},
  { -87.1984468409600f,    16.2307484204660f},
  { -95.3688249995255f,    -8.32049310088982f},
  { -145.141668662540f,    7.09722820828551f},
  { -76.1747388626429f,    -26.0346292529495f},
  { 8.43508465991598f,    -22.2536807628812f},
  { -141.973212055467f,    -51.0631446176492f},
  { 45.4894111866166f,    53.0301087283333f},
  { 121.060252533192f,    -24.3604465755772f},
  { 35.1102807278217f,    -3.63043247728744f},
  { 88.8428357129855f,    57.4332893839137f},
  { -167.126059261710f,    19.4742624987016f},
  { -66.2625690068797f,    60.9970868696274f},
  { -14.8178344976734f,    -36.5260594395900f},
  { -115.387970361397f,    17.3394217540441f},
  { -110.890251669620f,    -34.3614248895857f},
  { -168.220408650410f,    47.5234113593310f},
  { 73.6594541420187f,    -72.6968850461988f},
  { 68.5830480771596f,    -47.3475133162258f},
  { 7.93890320933269f,    35.0753303023187f},
  { -43.4439518579995f,    -17.9788426534101f},
  { 35.6740711982305f,    26.0564016491644f},
  { 70.9321750371959f,    33.0825830908537f},
  { 134.656541011646f,    17.1789935714075f},
  { -5.03841896304192f,    59.4959374463847f},
  { 102.628200263833f,    27.7025093945753f},
  { 147.788733676045f,    -39.2424523463052f},
  { 86.3561988821177f,    5.29464568902442f},
  { -63.0081687305366f,    30.9786820671334f},
  { -98.3367463783032f,    43.9756566918809f},
  { -64.3660787049967f,    -0.501498498922107f},
  { 91.9769148523511f,    -23.7256093385723f},
  { -119.020522782526f,    -77.8191277346684f},
  { -16.2582503946322f,    -9.32717994693467f},
  { -121.931148381790f,    -8.44253311125268f},
  { 38.7090286390384f,    -29.2535061459944f},
  { 141.400254260336f,    -7.35391330050412f},
  { -32.6826585498524f,    38.9130016141050f},
  { 35.6780819027964f,    84.4425198463807f},
  { -136.278011571866f,    35.4901517459935f},
  { -168.197490338604f,    -7.48798542456473f},
  { -41.5812660660292f,    9.18909711830814f},
  { 129.196253224049f,    44.6334122406911f},
  { 161.327726374986f,    35.0128779026495f},
  { -23.4689242463536f,    -66.8985521594749f}};
 
/* Sphere Covering (61 points) */
const float __SphCovering_61_dirs_deg[61][2] =
{ { -154.755900464835f,    -2.67044169154574f},
  { -127.918557340908f,    -13.9337606197865f},
  { -89.3986047742623f,    47.3916310664509f},
  { 30.6847547182312f,    30.1839896052869f},
  { 56.8448617283144f,    -40.7304237402600f},
  { -27.3959769741803f,    -14.3818136155788f},
  { 137.028586283488f,    -58.6365007536885f},
  { 28.2181714101930f,    -1.63344537813846f},
  { 75.8710712312236f,    3.08423181118922f},
  { 68.2220846662271f,    34.2273527655251f},
  { -101.413529738156f,    -6.26586644755068f},
  { 177.542431977188f,    -51.2934736512918f},
  { 159.511450164421f,    -7.08405017899750f},
  { -127.557593929975f,    12.0601886297087f},
  { 7.35219442711872f,    17.3692155593909f},
  { 150.705088853260f,    18.7832753977738f},
  { -48.9890373992757f,    54.4241150438866f},
  { -6.69386592051341f,    42.1290137181743f},
  { 94.9964024326905f,    20.7754496514437f},
  { 21.0940141855364f,    -54.3015020757286f},
  { 0.778592347803276f,    -11.1572071445825f},
  { 176.625699504979f,    32.0993875144092f},
  { -128.835289813117f,    42.4407027587255f},
  { 22.9463867371943f,    -27.0487645503310f},
  { -166.862498675950f,    54.9747274850074f},
  { 85.3879002083466f,    -21.0900034809705f},
  { 73.3672456665019f,    63.3748617194204f},
  { 144.064508007694f,    48.1112660571352f},
  { 32.1102737125167f,    50.6540527519258f},
  { -46.7894524237684f,    -40.3568552578347f},
  { -111.394454529335f,    -34.7246801316987f},
  { -70.2388961050876f,    26.1635447568539f},
  { -57.1634262624071f,    -16.3023681448573f},
  { -11.4803553410363f,    -37.6387434777340f},
  { 106.209186483401f,    46.5310484581644f},
  { -133.367385972602f,    -56.2650284396420f},
  { -47.6649319347283f,    6.80330085938340f},
  { -177.187198144207f,    -23.3314143755223f},
  { -18.7626489171491f,    12.1787908933008f},
  { -178.928989841405f,    6.49218477662736f},
  { 124.687075376370f,    21.4968035155134f},
  { 92.5727909592871f,    -48.5048880623901f},
  { -7.71430375364140f,    72.4562427722439f},
  { 65.4432393598426f,    -72.3015441675586f},
  { -103.201158058964f,    21.5976440874564f},
  { 140.855944354962f,    75.0918486298457f},
  { -113.846713892495f,    72.1010089392628f},
  { -37.7327085561355f,    33.4464112907618f},
  { 149.839922582613f,    -33.2412924001050f},
  { -151.083240998047f,    -80.8787223606670f},
  { 53.8311037259262f,    -17.2380082243059f},
  { -80.9875843417419f,    -28.3975072000690f},
  { -152.492717174069f,    25.2095700279611f},
  { -79.8588574853341f,    -56.8482994750852f},
  { -149.880029628272f,    -32.2913283757781f},
  { -78.9134771233683f,    2.85436114378274f},
  { -30.5953733021908f,    -66.3886197218085f},
  { 51.2831604109795f,    12.1879582180229f},
  { 117.765745211189f,    -30.2470149627513f},
  { 106.982679506827f,    -3.89800376761353f},
  { 132.410546454733f,    -6.75173465782162f}};
 
/* Sphere Covering (62 points) */
const float __SphCovering_62_dirs_deg[62][2] =
{ { 64.7499604277343f,    15.2338018569383f},
  { -68.5028339858412f,    -53.4053960841440f},
  { 5.27688399737537f,    10.4198104622492f},
  { 165.338430940902f,    -5.52680818761143f},
  { 55.9871439090035f,    40.6015082363555f},
  { -11.5989576046284f,    86.3905763498255f},
  { 148.310125269614f,    17.3841124620643f},
  { -34.7756733754653f,    -70.7430989648027f},
  { 157.609230284587f,    -30.0888786112952f},
  { -91.0945598478496f,    40.1494445359973f},
  { 177.817451718851f,    20.6453882319490f},
  { 0.660219267329248f,    -48.4200903087107f},
  { 22.0393945475022f,    -7.63867332468413f},
  { 32.5434298056356f,    61.1174080066049f},
  { -17.9267034940532f,    55.0572334075062f},
  { 28.8936886506523f,    -33.5730349634857f},
  { 125.873098012291f,    42.6824909482707f},
  { 77.0800121789496f,    -11.4064437854644f},
  { -17.0924769443427f,    30.4968245614283f},
  { -87.8344299935552f,    -10.5785197715004f},
  { -173.067631597216f,    -53.8608975312730f},
  { 90.7164077030632f,    35.1675765073348f},
  { 136.106124233327f,    -7.67706149695790f},
  { -151.982784736402f,    19.6856839251048f},
  { -159.305185358174f,    44.7720680271128f},
  { 59.4672895566281f,    -36.2132244834486f},
  { 93.8275685306236f,    -56.6660988962335f},
  { -36.1553557461403f,    -19.2141396597122f},
  { -122.893717477610f,    35.7124593705042f},
  { 93.4780642755938f,    -31.2892251920943f},
  { 49.4628734958488f,    -9.16102218634673f},
  { 160.267754453994f,    66.6579098855200f},
  { -67.9298761907104f,    -30.0075186043866f},
  { -101.253101555519f,    -37.7900043356486f},
  { 151.060322686242f,    -83.3768183474374f},
  { -2.72263814668216f,    -20.4992839941906f},
  { -52.2262489417648f,    35.8860655824289f},
  { 108.861981074856f,    -7.74123277001255f},
  { 44.3973536290972f,    -63.0196278864393f},
  { -31.1356725029992f,    -39.1759892420700f},
  { -167.091681794002f,    -4.19164463761808f},
  { 36.5025681699896f,    17.2718127342187f},
  { -116.293243677703f,    -14.2173747283762f},
  { -146.195911005581f,    -12.1197762404023f},
  { 143.858243201447f,    -55.7705658624441f},
  { -129.860884266401f,    9.25957092710923f},
  { -41.9622829997912f,    11.9708072136683f},
  { 92.5154951797740f,    10.5412775148169f},
  { 119.885689053173f,    17.9330060297996f},
  { 94.1369657399943f,    61.1345967404588f},
  { -18.4979424157986f,    0.890204526294760f},
  { 161.058436211274f,    41.4271404191390f},
  { -60.1949459564443f,    -4.55621768265982f},
  { -128.697779942286f,    62.5498024944320f},
  { -74.1579274237825f,    17.1881608961296f},
  { 125.718399407605f,    -33.7340361039175f},
  { -68.8924452865302f,    61.9195489197881f},
  { -137.372360960566f,    -37.1683451279316f},
  { 17.1354487789775f,    35.6345371103664f},
  { -101.751574837283f,    12.3735965436453f},
  { -171.686803310951f,    -28.5539246781397f},
  { -122.687452671363f,    -63.6842589287910f}};
 
/* Sphere Covering (63 points) */
const float __SphCovering_63_dirs_deg[63][2] =
{ { 155.288751214307f,    26.4070518197845f},
  { 63.2774588942481f,    -25.4444827239647f},
  { -34.9779274771465f,    1.93149802316552f},
  { 16.8277704429923f,    33.6228822916621f},
  { -18.8457277974430f,    49.6187180161244f},
  { -11.6098438027359f,    23.5852346787652f},
  { 53.7325549851637f,    44.2936482681786f},
  { -52.9424461856783f,    51.1748713876997f},
  { -43.8633569640353f,    -48.7999613268825f},
  { -145.084372883027f,    35.1790356632374f},
  { -24.0246933076306f,    -26.8522400266012f},
  { 74.9657979149169f,    -48.6996937127346f},
  { 36.8549372139951f,    -63.9993857161130f},
  { 34.4330446139771f,    -37.2835096447529f},
  { -127.196630519043f,    10.0044160607793f},
  { 166.576019778384f,    71.1613581552483f},
  { 19.1247582436717f,    61.1804333640693f},
  { 125.237114859695f,    24.4148775661146f},
  { 115.508291498374f,    -74.9486091810630f},
  { -95.9303236387537f,    11.3256567363510f},
  { -10.2725603089005f,    -3.35243335508996f},
  { 13.7727594793547f,    6.12721066112902f},
  { -151.896841067133f,    6.51338421504720f},
  { -41.9943686363186f,    25.4313046946767f},
  { -135.401386145316f,    59.9313853706841f},
  { -95.8329208135815f,    -60.0860839753694f},
  { 168.197490338604f,    2.37210256762112f},
  { 98.4341492034754f,    16.4587856229280f},
  { -42.6744695391388f,    -76.7133191900659f},
  { 115.227542178760f,    -4.62462884339844f},
  { -170.426296161663f,    -13.8180231451701f},
  { 83.8695620512499f,    -4.62955628043657f},
  { -135.796727023956f,    -43.9223716169338f},
  { 71.0410370182708f,    24.0653733110848f},
  { 96.6121434149594f,    43.9487276755098f},
  { 159.746362860425f,    -22.6610537552192f},
  { -49.8100859196981f,    79.6984293026975f},
  { 158.153540189961f,    -49.0898779712187f},
  { -140.918969712426f,    -18.3999666328313f},
  { 97.1621828982850f,    -25.9481126258847f},
  { 58.8599542937895f,    -0.0703191101964059f},
  { -75.4871895084860f,    29.3761191141524f},
  { 34.0050451410144f,    -11.5216083022857f},
  { -172.809800589408f,    17.9421733545217f},
  { -51.8910686316133f,    -18.9127638594733f},
  { -169.182977746229f,    -37.3035631675825f},
  { -64.5780730891951f,    6.15127488852452f},
  { -108.501017663924f,    -31.0205079861779f},
  { -75.7564796721975f,    -36.9941659582119f},
  { -5.04827383711817f,    -49.5362120936256f},
  { 140.254338670074f,    0.632488110044916f},
  { 8.92782836372849f,    -24.0458927460504f},
  { -179.542054682195f,    43.9831051432177f},
  { 38.8746134418312f,    18.3335035285961f},
  { -111.904386967001f,    33.1255549254886f},
  { 136.346766507282f,    49.2898402417193f},
  { 84.8665086147775f,    67.9986311261261f},
  { 116.608370465025f,    -49.3557303881594f},
  { 131.150039305445f,    -26.0615582693206f},
  { -161.843388390604f,    -67.6777747608528f},
  { -95.8902165930946f,    53.7468789300420f},
  { -82.7694830845987f,    -11.8184004401635f},
  { -113.611801196491f,    -9.61079405552443f}};
 
/* Sphere Covering (64 points) */
const float __SphCovering_64_dirs_deg[64][2] =
{ { 102.009405845092f,    -77.6930770197396f},
  { 113.130516648581f,    11.4815012566266f},
  { 73.1323329704983f,    55.0515038295549f},
  { 5.30450056310067f,    4.57730252952063f},
  { 82.8382380200144f,    14.7708519584726f},
  { -27.6830288295409f,    34.1849538886854f},
  { 94.6297094438068f,    35.8728875531408f},
  { -124.893340182617f,    -28.4502193172210f},
  { 29.0151557032200f,    49.8874352220408f},
  { 160.703202378293f,    43.2846695909532f},
  { -163.000763136768f,    14.9301342255190f},
  { -13.0491137841045f,    -16.8678774886514f},
  { -67.4199437530440f,    -9.13065542320480f},
  { 176.786127687616f,    -33.7454952598201f},
  { 127.082038960017f,    36.3507343542800f},
  { -104.266859557907f,    -49.6061129446315f},
  { 72.9375273201538f,    -12.3798990793917f},
  { -148.951838000160f,    -51.5879739579891f},
  { -55.7344695213508f,    46.7865876347928f},
  { 24.0321417589673f,    -46.7384591800018f},
  { -83.9726944543735f,    71.2931384481283f},
  { 144.350986905260f,    -34.1964130445881f},
  { 12.9706185661716f,    -24.3243502344840f},
  { -73.3958935562585f,    -34.7596305572017f},
  { 30.6985057053144f,    -5.05761304917880f},
  { 143.812406577837f,    15.9133298019635f},
  { 130.794805472464f,    -7.91483898193719f},
  { -119.215328432870f,    -75.3038430140441f},
  { 123.816179527771f,    61.1747037861180f},
  { 4.48104561993866f,    -71.1384398434430f},
  { -73.9344738836814f,    20.6946626023302f},
  { 63.5295603241057f,    -53.3423707266797f},
  { -135.252417118582f,    24.9408528220447f},
  { -107.870764089280f,    24.8291260519942f},
  { -166.449969063455f,    40.0245397366588f},
  { 57.9203035097749f,    30.1920110144187f},
  { 115.892173221112f,    -53.6236930040889f},
  { 48.1273088753989f,    79.5838377436714f},
  { 158.216565547426f,    -9.81533998838613f},
  { 47.1343730164372f,    -26.0266078438176f},
  { -54.8996700138452f,    -59.0031937425722f},
  { 112.311187001544f,    -27.9597674445890f},
  { -175.428217713155f,    -6.72022197908943f},
  { 169.452267909941f,    17.1830042759734f},
  { 165.561884481003f,    -59.0604895220853f},
  { -130.536974464656f,    50.8563068536070f},
  { 55.0686925634088f,    3.78684995535815f},
  { 81.0219618094497f,    -35.8614283972382f},
  { -14.4425471418627f,    60.3267262493244f},
  { -43.2560217011966f,    -30.2240966509461f},
  { -16.0262024876043f,    -43.7258470932039f},
  { -92.3951740427966f,    43.5820346866261f},
  { -173.205141468048f,    69.2190312297548f},
  { 99.1446168694376f,    -9.04700358511570f},
  { 29.9754329678593f,    21.9081872124173f},
  { -144.184829144672f,    -3.33461436766139f},
  { -20.4345397633408f,    11.4052978698742f},
  { -155.134052609622f,    -25.1104483294035f},
  { -92.2003683924521f,    3.70720882183497f},
  { -39.6687329458825f,    -6.36326927272292f},
  { -120.676370810454f,    -1.14614477337970f},
  { -97.3226110809217f,    -19.7750653411452f},
  { -51.8326269365099f,    16.5172273180314f},
  { 2.49465823999960f,    32.1039711767703f}};
 
/* sphere covering handles */
const float* __HANDLES_SphCovering_dirs_deg[64] =
{ NULL, /* sphere covering not defined for 1 point */
  NULL, /* sphere covering not defined for 2 points */
  NULL, /* sphere covering not defined for 3 points */
  &__SphCovering_4_dirs_deg[0][0],
  &__SphCovering_5_dirs_deg[0][0],
  &__SphCovering_6_dirs_deg[0][0],
  &__SphCovering_7_dirs_deg[0][0],
  &__SphCovering_8_dirs_deg[0][0],
  &__SphCovering_9_dirs_deg[0][0],
  &__SphCovering_10_dirs_deg[0][0],
  &__SphCovering_11_dirs_deg[0][0],
  &__SphCovering_12_dirs_deg[0][0],
  &__SphCovering_13_dirs_deg[0][0],
  &__SphCovering_14_dirs_deg[0][0],
  &__SphCovering_15_dirs_deg[0][0],
  &__SphCovering_16_dirs_deg[0][0],
  &__SphCovering_17_dirs_deg[0][0],
  &__SphCovering_18_dirs_deg[0][0],
  &__SphCovering_19_dirs_deg[0][0],
  &__SphCovering_20_dirs_deg[0][0],
  &__SphCovering_21_dirs_deg[0][0],
  &__SphCovering_22_dirs_deg[0][0],
  &__SphCovering_23_dirs_deg[0][0],
  &__SphCovering_24_dirs_deg[0][0],
  &__SphCovering_25_dirs_deg[0][0],
  &__SphCovering_26_dirs_deg[0][0],
  &__SphCovering_27_dirs_deg[0][0],
  &__SphCovering_28_dirs_deg[0][0],
  &__SphCovering_29_dirs_deg[0][0],
  &__SphCovering_30_dirs_deg[0][0],
  &__SphCovering_31_dirs_deg[0][0],
  &__SphCovering_32_dirs_deg[0][0],
  &__SphCovering_33_dirs_deg[0][0],
  &__SphCovering_34_dirs_deg[0][0],
  &__SphCovering_35_dirs_deg[0][0],
  &__SphCovering_36_dirs_deg[0][0],
  &__SphCovering_37_dirs_deg[0][0],
  &__SphCovering_38_dirs_deg[0][0],
  &__SphCovering_39_dirs_deg[0][0],
  &__SphCovering_40_dirs_deg[0][0],
  &__SphCovering_41_dirs_deg[0][0],
  &__SphCovering_42_dirs_deg[0][0],
  &__SphCovering_43_dirs_deg[0][0],
  &__SphCovering_44_dirs_deg[0][0],
  &__SphCovering_45_dirs_deg[0][0],
  &__SphCovering_46_dirs_deg[0][0],
  &__SphCovering_47_dirs_deg[0][0],
  &__SphCovering_48_dirs_deg[0][0],
  &__SphCovering_49_dirs_deg[0][0],
  &__SphCovering_50_dirs_deg[0][0],
  &__SphCovering_51_dirs_deg[0][0],
  &__SphCovering_52_dirs_deg[0][0],
  &__SphCovering_53_dirs_deg[0][0],
  &__SphCovering_54_dirs_deg[0][0],
  &__SphCovering_55_dirs_deg[0][0],
  &__SphCovering_56_dirs_deg[0][0],
  &__SphCovering_57_dirs_deg[0][0],
  &__SphCovering_58_dirs_deg[0][0],
  &__SphCovering_59_dirs_deg[0][0],
  &__SphCovering_60_dirs_deg[0][0],
  &__SphCovering_61_dirs_deg[0][0],
  &__SphCovering_62_dirs_deg[0][0],
  &__SphCovering_63_dirs_deg[0][0],
  &__SphCovering_64_dirs_deg[0][0]};
 
/* 3LD geosphere 'ico' [0 0] (12 points) */
const float __geosphere_ico_0_0_dirs_deg[12][2] =
{ { 31.7174744114610f,    0.0f},
  { 148.282525588539f,    0.0f},
  { -148.282525588539f,    0.0f},
  { -31.7174744114610f,    0.0f},
  { 0.0f,    58.2825255885390f},
  { 0.0f,    -58.2825255885390f},
  { 180.0f,    -58.2825255885390f},
  { 180.0f,    58.2825255885390f},
  { 90.0f,    31.7174744114610f},
  { -90.0f,    31.7174744114610f},
  { -90.0f,    -31.7174744114610f},
  { 90.0f,    -31.7174744114610f}};
 
/* 3LD geosphere 'ico' [1 0] (32 points) */
const float __geosphere_ico_1_0_dirs_deg[32][2] =
{ { 31.7174744114610f,    0.0f},
  { 148.282525588539f,    0.0f},
  { -148.282525588539f,    0.0f},
  { -31.7174744114610f,    0.0f},
  { 0.0f,    58.2825255885390f},
  { 0.0f,    -58.2825255885390f},
  { 180.0f,    -58.2825255885390f},
  { 180.0f,    58.2825255885390f},
  { 90.0f,    31.7174744114610f},
  { -90.0f,    31.7174744114610f},
  { -90.0f,    -31.7174744114610f},
  { 90.0f,    -31.7174744114610f},
  { 90.0f,    69.0948425521107f},
  { -90.0f,    69.0948425521107f},
  { 90.0f,    -69.0948425521107f},
  { -90.0f,    -69.0948425521107f},
  { 0.0f,    20.9051574478893f},
  { 0.0f,    -20.9051574478893f},
  { 180.0f,    20.9051574478893f},
  { 180.0f,    -20.9051574478893f},
  { 69.0948425521107f,    0.0f},
  { 110.905157447889f,    0.0f},
  { -69.0948425521107f,    0.0f},
  { -110.905157447889f,    0.0f},
  { 45.0000000000000f,    35.2643896827547f},
  { 45.0000000000000f,    -35.2643896827547f},
  { -45.0000000000000f,    35.2643896827547f},
  { -45.0000000000000f,    -35.2643896827547f},
  { 135.0f,    35.2643896827547f},
  { 135.0f,    -35.2643896827547f},
  { -135.0f,    35.2643896827547f},
  { -135.0f,    -35.2643896827547f}};
 
/* 3LD geosphere 'ico' [2 0] (42 points) */
const float __geosphere_ico_2_0_dirs_deg[42][2] =
{ { 31.7174744114610f,    0.0f},
  { 148.282525588539f,    0.0f},
  { -148.282525588539f,    0.0f},
  { -31.7174744114610f,    0.0f},
  { 0.0f,    58.2825255885390f},
  { 0.0f,    -58.2825255885390f},
  { 180.0f,    -58.2825255885390f},
  { 180.0f,    58.2825255885390f},
  { 90.0f,    31.7174744114610f},
  { -90.0f,    31.7174744114610f},
  { -90.0f,    -31.7174744114610f},
  { 90.0f,    -31.7174744114610f},
  { 0.0f,    90.0f},
  { 58.2825255885390f,    54.0f},
  { 121.717474411461f,    54.0f},
  { -58.2825255885390f,    54.0f},
  { -121.717474411461f,    54.0f},
  { 58.2825255885390f,    -54.0f},
  { 0.0f,    -90.0f},
  { 121.717474411461f,    -54.0f},
  { -58.2825255885390f,    -54.0f},
  { -121.717474411461f,    -54.0f},
  { 0.0f,    0.0f},
  { 20.9051574478893f,    30.0000000000000f},
  { -20.9051574478893f,    30.0000000000000f},
  { 20.9051574478893f,    -30.0000000000000f},
  { -20.9051574478893f,    -30.0000000000000f},
  { 180.0f,    0.0f},
  { -159.094842552111f,    30.0000000000000f},
  { 159.094842552111f,    30.0000000000000f},
  { -159.094842552111f,    -30.0000000000000f},
  { 159.094842552111f,    -30.0000000000000f},
  { 90.0f,    0.0f},
  { 58.2825255885390f,    18.0f},
  { 58.2825255885390f,    -18.0f},
  { 121.717474411461f,    18.0f},
  { 121.717474411461f,    -18.0f},
  { -58.2825255885390f,    18.0f},
  { -90.0f,    0.0f},
  { -58.2825255885390f,    -18.0f},
  { -121.717474411461f,    18.0f},
  { -121.717474411461f,    -18.0f}};
 
/* 3LD geosphere 'ico' [3 0] (92 points) */
const float __geosphere_ico_3_0_dirs_deg[92][2] =
{ { 31.7174744114610f,    0.0f},
  { 148.282525588539f,    0.0f},
  { -148.282525588539f,    0.0f},
  { -31.7174744114610f,    0.0f},
  { 0.0f,    58.2825255885390f},
  { 0.0f,    -58.2825255885390f},
  { 180.0f,    -58.2825255885390f},
  { 180.0f,    58.2825255885390f},
  { 90.0f,    31.7174744114610f},
  { -90.0f,    31.7174744114610f},
  { -90.0f,    -31.7174744114610f},
  { 90.0f,    -31.7174744114610f},
  { 0.0f,    78.3592768632294f},
  { 180.0f,    78.3592768632294f},
  { 38.9734473368657f,    58.7297899739513f},
  { 90.0f,    69.0948425521107f},
  { 141.026552663134f,    58.7297899739513f},
  { 72.8279621494862f,    46.8885380691238f},
  { 107.172037850514f,    46.8885380691238f},
  { -38.9734473368657f,    58.7297899739513f},
  { -72.8279621494862f,    46.8885380691238f},
  { -90.0f,    69.0948425521107f},
  { -107.172037850514f,    46.8885380691238f},
  { -141.026552663134f,    58.7297899739513f},
  { 38.9734473368657f,    -58.7297899739513f},
  { 72.8279621494862f,    -46.8885380691238f},
  { 0.0f,    -78.3592768632294f},
  { 90.0f,    -69.0948425521107f},
  { 107.172037850514f,    -46.8885380691238f},
  { 180.0f,    -78.3592768632294f},
  { 141.026552663134f,    -58.7297899739513f},
  { -38.9734473368657f,    -58.7297899739513f},
  { -90.0f,    -69.0948425521107f},
  { -141.026552663134f,    -58.7297899739513f},
  { -72.8279621494862f,    -46.8885380691238f},
  { -107.172037850514f,    -46.8885380691238f},
  { 11.6407231367706f,    0.0f},
  { -11.6407231367706f,    0.0f},
  { 25.2736805860404f,    19.0551045548580f},
  { 0.0f,    20.9051574478893f},
  { -25.2736805860404f,    19.0551045548580f},
  { 15.4504370863258f,    40.7647476003615f},
  { -15.4504370863258f,    40.7647476003615f},
  { 25.2736805860404f,    -19.0551045548580f},
  { 15.4504370863258f,    -40.7647476003615f},
  { 0.0f,    -20.9051574478893f},
  { -15.4504370863258f,    -40.7647476003615f},
  { -25.2736805860404f,    -19.0551045548580f},
  { -168.359276863229f,    0.0f},
  { 168.359276863229f,    0.0f},
  { -154.726319413960f,    19.0551045548580f},
  { 180.0f,    20.9051574478893f},
  { 154.726319413960f,    19.0551045548580f},
  { -164.549562913674f,    40.7647476003615f},
  { 164.549562913674f,    40.7647476003615f},
  { -154.726319413960f,    -19.0551045548580f},
  { -164.549562913674f,    -40.7647476003615f},
  { 180.0f,    -20.9051574478893f},
  { 164.549562913674f,    -40.7647476003615f},
  { 154.726319413960f,    -19.0551045548580f},
  { 90.0f,    11.6407231367706f},
  { 90.0f,    -11.6407231367706f},
  { 69.0948425521107f,    23.8001826021751f},
  { 69.0948425521107f,    0.0f},
  { 69.0948425521107f,    -23.8001826021751f},
  { 48.1896851042214f,    11.6407231367706f},
  { 48.1896851042214f,    -11.6407231367706f},
  { 110.905157447889f,    23.8001826021751f},
  { 131.810314895779f,    11.6407231367706f},
  { 110.905157447889f,    0.0f},
  { 131.810314895779f,    -11.6407231367706f},
  { 110.905157447889f,    -23.8001826021751f},
  { -69.0948425521107f,    23.8001826021751f},
  { -48.1896851042214f,    11.6407231367706f},
  { -90.0f,    11.6407231367706f},
  { -69.0948425521107f,    0.0f},
  { -48.1896851042214f,    -11.6407231367706f},
  { -90.0f,    -11.6407231367706f},
  { -69.0948425521107f,    -23.8001826021751f},
  { -110.905157447889f,    23.8001826021751f},
  { -110.905157447889f,    0.0f},
  { -110.905157447889f,    -23.8001826021751f},
  { -131.810314895779f,    11.6407231367706f},
  { -131.810314895779f,    -11.6407231367706f},
  { 45.0000000000000f,    35.2643896827547f},
  { 45.0000000000000f,    -35.2643896827547f},
  { -45.0000000000000f,    35.2643896827547f},
  { -45.0000000000000f,    -35.2643896827547f},
  { 135.0f,    35.2643896827547f},
  { 135.0f,    -35.2643896827547f},
  { -135.0f,    35.2643896827547f},
  { -135.0f,    -35.2643896827547f}};
 
/* 3LD geosphere 'ico' [4 0] (162 points) */
const float __geosphere_ico_4_0_dirs_deg[162][2] =
{ { 31.7174744114610f,    0.0f},
  { 148.282525588539f,    0.0f},
  { -148.282525588539f,    0.0f},
  { -31.7174744114610f,    0.0f},
  { 0.0f,    58.2825255885390f},
  { 0.0f,    -58.2825255885390f},
  { 180.0f,    -58.2825255885390f},
  { 180.0f,    58.2825255885390f},
  { 90.0f,    31.7174744114610f},
  { -90.0f,    31.7174744114610f},
  { -90.0f,    -31.7174744114610f},
  { 90.0f,    -31.7174744114610f},
  { 0.0f,    72.8279621494862f},
  { 0.0f,    90.0f},
  { 180.0f,    72.8279621494862f},
  { 28.3399673707642f,    59.7900946927798f},
  { 58.2825255885390f,    72.0f},
  { 121.717474411461f,    72.0f},
  { 151.660032629236f,    59.7900946927798f},
  { 58.2825255885390f,    54.0f},
  { 90.0f,    58.2825255885390f},
  { 121.717474411461f,    54.0f},
  { 78.3592768632294f,    42.9780676586279f},
  { 101.640723136771f,    42.9780676586279f},
  { -28.3399673707642f,    59.7900946927798f},
  { -58.2825255885390f,    54.0f},
  { -78.3592768632294f,    42.9780676586279f},
  { -58.2825255885390f,    72.0f},
  { -90.0f,    58.2825255885390f},
  { -101.640723136771f,    42.9780676586279f},
  { -121.717474411461f,    72.0f},
  { -121.717474411461f,    54.0f},
  { -151.660032629236f,    59.7900946927798f},
  { 28.3399673707642f,    -59.7900946927798f},
  { 58.2825255885390f,    -54.0f},
  { 78.3592768632294f,    -42.9780676586279f},
  { 0.0f,    -72.8279621494862f},
  { 58.2825255885390f,    -72.0f},
  { 90.0f,    -58.2825255885390f},
  { 101.640723136771f,    -42.9780676586279f},
  { 0.0f,    -90.0f},
  { 121.717474411461f,    -72.0f},
  { 121.717474411461f,    -54.0f},
  { 180.0f,    -72.8279621494862f},
  { 151.660032629236f,    -59.7900946927798f},
  { -28.3399673707642f,    -59.7900946927798f},
  { -58.2825255885390f,    -72.0f},
  { -121.717474411461f,    -72.0f},
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  { -58.2825255885390f,    -54.0f},
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  { 17.1720378505138f,    0.0f},
  { 0.0f,    0.0f},
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  { 27.1333780408531f,    13.8190092060518f},
  { 9.69372389531482f,    15.2401622826778f},
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  { 20.9051574478893f,    30.0000000000000f},
  { 0.0f,    31.7174744114610f},
  { -20.9051574478893f,    30.0000000000000f},
  { 12.2183198662487f,    45.7717617455715f},
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  { 0.0f,    -31.7174744114610f},
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  { -9.69372389531481f,    -15.2401622826778f},
  { -20.9051574478893f,    -30.0000000000000f},
  { -27.1333780408531f,    -13.8190092060518f},
  { -162.827962149486f,    0.0f},
  { 180.0f,    0.0f},
  { 162.827962149486f,    0.0f},
  { -152.866621959147f,    13.8190092060518f},
  { -170.306276104685f,    15.2401622826778f},
  { 170.306276104685f,    15.2401622826778f},
  { 152.866621959147f,    13.8190092060518f},
  { -159.094842552111f,    30.0000000000000f},
  { 180.0f,    31.7174744114610f},
  { 159.094842552111f,    30.0000000000000f},
  { -167.781680133751f,    45.7717617455715f},
  { 167.781680133751f,    45.7717617455715f},
  { -152.866621959147f,    -13.8190092060518f},
  { -159.094842552111f,    -30.0000000000000f},
  { -167.781680133751f,    -45.7717617455715f},
  { -170.306276104685f,    -15.2401622826778f},
  { 180.0f,    -31.7174744114610f},
  { 167.781680133751f,    -45.7717617455715f},
  { 170.306276104685f,    -15.2401622826778f},
  { 159.094842552111f,    -30.0000000000000f},
  { 152.866621959147f,    -13.8190092060518f},
  { 90.0f,    17.1720378505138f},
  { 90.0f,    0.0f},
  { 90.0f,    -17.1720378505138f},
  { 74.5495629136742f,    26.2866766550738f},
  { 74.5495629136742f,    9.34970354257458f},
  { 74.5495629136742f,    -9.34970354257458f},
  { 74.5495629136742f,    -26.2866766550738f},
  { 58.2825255885390f,    18.0f},
  { 58.2825255885390f,    0.0f},
  { 58.2825255885390f,    -18.0f},
  { 43.5723495188822f,    8.48907956344660f},
  { 43.5723495188822f,    -8.48907956344660f},
  { 105.450437086326f,    26.2866766550738f},
  { 121.717474411461f,    18.0f},
  { 136.427650481118f,    8.48907956344661f},
  { 105.450437086326f,    9.34970354257458f},
  { 121.717474411461f,    0.0f},
  { 136.427650481118f,    -8.48907956344661f},
  { 105.450437086326f,    -9.34970354257458f},
  { 121.717474411461f,    -18.0f},
  { 105.450437086326f,    -26.2866766550738f},
  { -74.5495629136742f,    26.2866766550738f},
  { -58.2825255885390f,    18.0f},
  { -43.5723495188822f,    8.48907956344660f},
  { -90.0f,    17.1720378505138f},
  { -74.5495629136742f,    9.34970354257458f},
  { -58.2825255885390f,    0.0f},
  { -43.5723495188822f,    -8.48907956344661f},
  { -90.0f,    0.0f},
  { -74.5495629136742f,    -9.34970354257458f},
  { -58.2825255885390f,    -18.0f},
  { -90.0f,    -17.1720378505138f},
  { -74.5495629136742f,    -26.2866766550738f},
  { -105.450437086326f,    26.2866766550738f},
  { -105.450437086326f,    9.34970354257458f},
  { -105.450437086326f,    -9.34970354257458f},
  { -105.450437086326f,    -26.2866766550738f},
  { -121.717474411461f,    18.0f},
  { -121.717474411461f,    0.0f},
  { -121.717474411461f,    -18.0f},
  { -136.427650481118f,    8.48907956344661f},
  { -136.427650481118f,    -8.48907956344661f},
  { 58.2825255885390f,    36.0f},
  { 40.5007050124200f,    25.1712621719368f},
  { 35.8897546595841f,    43.4870777455218f},
  { 58.2825255885390f,    -36.0f},
  { 35.8897546595841f,    -43.4870777455218f},
  { 40.5007050124200f,    -25.1712621719368f},
  { -35.8897546595841f,    43.4870777455218f},
  { -40.5007050124200f,    25.1712621719368f},
  { -58.2825255885390f,    36.0f},
  { -35.8897546595841f,    -43.4870777455218f},
  { -58.2825255885390f,    -36.0f},
  { -40.5007050124200f,    -25.1712621719368f},
  { 144.110245340416f,    43.4870777455218f},
  { 139.499294987580f,    25.1712621719368f},
  { 121.717474411461f,    36.0f},
  { 144.110245340416f,    -43.4870777455218f},
  { 121.717474411461f,    -36.0f},
  { 139.499294987580f,    -25.1712621719368f},
  { -144.110245340416f,    43.4870777455218f},
  { -121.717474411461f,    36.0f},
  { -139.499294987580f,    25.1712621719368f},
  { -144.110245340416f,    -43.4870777455218f},
  { -139.499294987580f,    -25.1712621719368f},
  { -121.717474411461f,    -36.0f}};
 
/* 3LD geosphere 'ico' [5 0] (252 points) */
const float __geosphere_ico_5_0_dirs_deg[252][2] =
{ { 31.7174744114610f,    0.0f},
  { 148.282525588539f,    0.0f},
  { -148.282525588539f,    0.0f},
  { -31.7174744114610f,    0.0f},
  { 0.0f,    58.2825255885390f},
  { 0.0f,    -58.2825255885390f},
  { 180.0f,    -58.2825255885390f},
  { 180.0f,    58.2825255885390f},
  { 90.0f,    31.7174744114610f},
  { -90.0f,    31.7174744114610f},
  { -90.0f,    -31.7174744114610f},
  { 90.0f,    -31.7174744114610f},
  { 0.0f,    69.6541923856616f},
  { 0.0f,    82.9535936191428f},
  { 180.0f,    82.9535936191428f},
  { 180.0f,    69.6541923856616f},
  { 22.0237505161462f,    59.9952713133382f},
  { 38.9734473368657f,    71.0021166134344f},
  { 90.0f,    77.7816801337513f},
  { 141.026552663134f,    71.0021166134344f},
  { 157.976249483854f,    59.9952713133382f},
  { 47.1679114977868f,    57.2262493118836f},
  { 72.8279621494862f,    63.7030502822517f},
  { 107.172037850514f,    63.7030502822517f},
  { 132.832088502213f,    57.2262493118836f},
  { 67.6072290710451f,    49.9068566415137f},
  { 90.0f,    52.1031151288303f},
  { 112.392770928955f,    49.9068566415137f},
  { 81.2167693990410f,    40.6247965576687f},
  { 98.7832306009590f,    40.6247965576687f},
  { -22.0237505161462f,    59.9952713133382f},
  { -47.1679114977868f,    57.2262493118836f},
  { -67.6072290710451f,    49.9068566415137f},
  { -81.2167693990410f,    40.6247965576687f},
  { -38.9734473368657f,    71.0021166134344f},
  { -72.8279621494862f,    63.7030502822517f},
  { -90.0f,    52.1031151288303f},
  { -98.7832306009590f,    40.6247965576687f},
  { -90.0000000000000f,    77.7816801337513f},
  { -107.172037850514f,    63.7030502822517f},
  { -112.392770928955f,    49.9068566415137f},
  { -141.026552663134f,    71.0021166134344f},
  { -132.832088502213f,    57.2262493118836f},
  { -157.976249483854f,    59.9952713133382f},
  { 22.0237505161462f,    -59.9952713133382f},
  { 47.1679114977868f,    -57.2262493118836f},
  { 67.6072290710451f,    -49.9068566415137f},
  { 81.2167693990410f,    -40.6247965576687f},
  { 0.0f,    -69.6541923856616f},
  { 38.9734473368657f,    -71.0021166134344f},
  { 72.8279621494862f,    -63.7030502822517f},
  { 90.0f,    -52.1031151288303f},
  { 98.7832306009590f,    -40.6247965576687f},
  { 0.0f,    -82.9535936191428f},
  { 90.0000000000000f,    -77.7816801337513f},
  { 107.172037850514f,    -63.7030502822517f},
  { 112.392770928955f,    -49.9068566415137f},
  { 180.0f,    -82.9535936191428f},
  { 141.026552663134f,    -71.0021166134344f},
  { 132.832088502213f,    -57.2262493118836f},
  { 180.0f,    -69.6541923856616f},
  { 157.976249483854f,    -59.9952713133382f},
  { -22.0237505161462f,    -59.9952713133382f},
  { -38.9734473368657f,    -71.0021166134344f},
  { -90.0f,    -77.7816801337513f},
  { -141.026552663134f,    -71.0021166134344f},
  { -157.976249483854f,    -59.9952713133382f},
  { -47.1679114977868f,    -57.2262493118836f},
  { -72.8279621494862f,    -63.7030502822517f},
  { -107.172037850514f,    -63.7030502822517f},
  { -132.832088502213f,    -57.2262493118836f},
  { -67.6072290710451f,    -49.9068566415137f},
  { -90.0f,    -52.1031151288303f},
  { -112.392770928955f,    -49.9068566415137f},
  { -81.2167693990410f,    -40.6247965576687f},
  { -98.7832306009590f,    -40.6247965576687f},
  { 20.3458076143384f,    0.0f},
  { 7.04640638085718f,    0.0f},
  { -7.04640638085718f,    0.0f},
  { -20.3458076143384f,    0.0f},
  { 28.1611303732939f,    10.8082208669889f},
  { 14.9845972116948f,    11.8147143864651f},
  { 0.0f,    12.2183198662487f},
  { -14.9845972116948f,    11.8147143864651f},
  { -28.1611303732939f,    10.8082208669889f},
  { 23.6387115659933f,    23.3894469911546f},
  { 8.30077479951012f,    25.0415008212998f},
  { -8.30077479951012f,    25.0415008212998f},
  { -23.6387115659933f,    23.3894469911546f},
  { 17.7818205761190f,    36.5460212963266f},
  { 0.0f,    37.8968848711697f},
  { -17.7818205761190f,    36.5460212963266f},
  { 10.0928404843176f,    48.5980887666628f},
  { -10.0928404843176f,    48.5980887666628f},
  { 28.1611303732939f,    -10.8082208669889f},
  { 23.6387115659933f,    -23.3894469911546f},
  { 17.7818205761190f,    -36.5460212963266f},
  { 10.0928404843176f,    -48.5980887666628f},
  { 14.9845972116948f,    -11.8147143864651f},
  { 8.30077479951012f,    -25.0415008212998f},
  { 0.0f,    -37.8968848711697f},
  { -10.0928404843176f,    -48.5980887666628f},
  { -1.01205574733119e-15f,    -12.2183198662487f},
  { -8.30077479951012f,    -25.0415008212998f},
  { -17.7818205761190f,    -36.5460212963266f},
  { -14.9845972116948f,    -11.8147143864651f},
  { -23.6387115659933f,    -23.3894469911546f},
  { -28.1611303732939f,    -10.8082208669889f},
  { -159.654192385662f,    0.0f},
  { -172.953593619143f,    0.0f},
  { 172.953593619143f,    0.0f},
  { 159.654192385662f,    0.0f},
  { -151.838869626706f,    10.8082208669889f},
  { -165.015402788305f,    11.8147143864651f},
  { 180.0f,    12.2183198662487f},
  { 165.015402788305f,    11.8147143864651f},
  { 151.838869626706f,    10.8082208669889f},
  { -156.361288434007f,    23.3894469911546f},
  { -171.699225200490f,    25.0415008212998f},
  { 171.699225200490f,    25.0415008212998f},
  { 156.361288434007f,    23.3894469911546f},
  { -162.218179423881f,    36.5460212963266f},
  { 180.0f,    37.8968848711697f},
  { 162.218179423881f,    36.5460212963266f},
  { -169.907159515682f,    48.5980887666628f},
  { 169.907159515682f,    48.5980887666628f},
  { -151.838869626706f,    -10.8082208669889f},
  { -156.361288434007f,    -23.3894469911546f},
  { -162.218179423881f,    -36.5460212963266f},
  { -169.907159515682f,    -48.5980887666628f},
  { -165.015402788305f,    -11.8147143864651f},
  { -171.699225200490f,    -25.0415008212998f},
  { 180.0f,    -37.8968848711697f},
  { 169.907159515682f,    -48.5980887666628f},
  { 180.0f,    -12.2183198662487f},
  { 171.699225200490f,    -25.0415008212998f},
  { 162.218179423881f,    -36.5460212963266f},
  { 165.015402788305f,    -11.8147143864651f},
  { 156.361288434007f,    -23.3894469911546f},
  { 151.838869626706f,    -10.8082208669889f},
  { 90.0f,    20.3458076143384f},
  { 90.0f,    7.04640638085718f},
  { 90.0f,    -7.04640638085718f},
  { 90.0f,    -20.3458076143384f},
  { 77.7816801337513f,    27.6183932347186f},
  { 77.7816801337513f,    14.6599491964913f},
  { 77.7816801337513f,    0.0f},
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  { 77.7816801337513f,    -27.6183932347186f},
  { 64.7263194139596f,    21.5935345276613f},
  { 64.7263194139596f,    7.51576871353677f},
  { 64.7263194139596f,    -7.51576871353677f},
  { 64.7263194139596f,    -21.5935345276613f},
  { 52.1031151288303f,    14.2023070245089f},
  { 52.1031151288303f,    0.0f},
  { 52.1031151288303f,    -14.2023070245089f},
  { 40.9590912848605f,    6.65525720600019f},
  { 40.9590912848605f,    -6.65525720600019f},
  { 102.218319866249f,    27.6183932347186f},
  { 115.273680586040f,    21.5935345276613f},
  { 127.896884871170f,    14.2023070245089f},
  { 139.040908715140f,    6.65525720600019f},
  { 102.218319866249f,    14.6599491964913f},
  { 115.273680586040f,    7.51576871353677f},
  { 127.896884871170f,    0.0f},
  { 139.040908715140f,    -6.65525720600019f},
  { 102.218319866249f,    -9.89130938771355e-16f},
  { 115.273680586040f,    -7.51576871353677f},
  { 127.896884871170f,    -14.2023070245090f},
  { 102.218319866249f,    -14.6599491964913f},
  { 115.273680586040f,    -21.5935345276613f},
  { 102.218319866249f,    -27.6183932347186f},
  { -77.7816801337513f,    27.6183932347186f},
  { -64.7263194139596f,    21.5935345276613f},
  { -52.1031151288303f,    14.2023070245089f},
  { -40.9590912848605f,    6.65525720600019f},
  { -90.0f,    20.3458076143384f},
  { -77.7816801337513f,    14.6599491964913f},
  { -64.7263194139596f,    7.51576871353677f},
  { -52.1031151288303f,    0.0f},
  { -40.9590912848605f,    -6.65525720600019f},
  { -90.0f,    7.04640638085718f},
  { -77.7816801337513f,    -9.89130938771355e-16f},
  { -64.7263194139596f,    -7.51576871353677f},
  { -52.1031151288303f,    -14.2023070245090f},
  { -90.0f,    -7.04640638085718f},
  { -77.7816801337513f,    -14.6599491964913f},
  { -64.7263194139596f,    -21.5935345276613f},
  { -90.0f,    -20.3458076143384f},
  { -77.7816801337513f,    -27.6183932347186f},
  { -102.218319866249f,    27.6183932347186f},
  { -102.218319866249f,    14.6599491964913f},
  { -102.218319866249f,    0.0f},
  { -102.218319866249f,    -14.6599491964913f},
  { -102.218319866249f,    -27.6183932347186f},
  { -115.273680586040f,    21.5935345276613f},
  { -115.273680586040f,    7.51576871353677f},
  { -115.273680586040f,    -7.51576871353677f},
  { -115.273680586040f,    -21.5935345276613f},
  { -127.896884871170f,    14.2023070245089f},
  { -127.896884871170f,    0.0f},
  { -127.896884871170f,    -14.2023070245089f},
  { -139.040908715140f,    6.65525720600019f},
  { -139.040908715140f,    -6.65525720600019f},
  { 65.9051574478893f,    35.7584993532105f},
  { 51.0265526631344f,    28.2445194108839f},
  { 38.2682973779569f,    19.3469890055802f},
  { 49.4992949875800f,    43.2255973783311f},
  { 34.6438140225457f,    33.6469345870906f},
  { 29.5495629136742f,    47.7981724013467f},
  { 65.9051574478893f,    -35.7584993532105f},
  { 49.4992949875800f,    -43.2255973783311f},
  { 29.5495629136742f,    -47.7981724013467f},
  { 51.0265526631344f,    -28.2445194108839f},
  { 34.6438140225457f,    -33.6469345870906f},
  { 38.2682973779569f,    -19.3469890055802f},
  { -29.5495629136742f,    47.7981724013467f},
  { -34.6438140225457f,    33.6469345870906f},
  { -38.2682973779569f,    19.3469890055802f},
  { -49.4992949875800f,    43.2255973783311f},
  { -51.0265526631344f,    28.2445194108839f},
  { -65.9051574478893f,    35.7584993532105f},
  { -29.5495629136742f,    -47.7981724013467f},
  { -49.4992949875800f,    -43.2255973783311f},
  { -65.9051574478893f,    -35.7584993532105f},
  { -34.6438140225457f,    -33.6469345870906f},
  { -51.0265526631344f,    -28.2445194108839f},
  { -38.2682973779569f,    -19.3469890055802f},
  { 150.450437086326f,    47.7981724013467f},
  { 145.356185977454f,    33.6469345870906f},
  { 141.731702622043f,    19.3469890055802f},
  { 130.500705012420f,    43.2255973783311f},
  { 128.973447336866f,    28.2445194108839f},
  { 114.094842552111f,    35.7584993532105f},
  { 150.450437086326f,    -47.7981724013467f},
  { 130.500705012420f,    -43.2255973783311f},
  { 114.094842552111f,    -35.7584993532105f},
  { 145.356185977454f,    -33.6469345870906f},
  { 128.973447336866f,    -28.2445194108839f},
  { 141.731702622043f,    -19.3469890055802f},
  { -150.450437086326f,    47.7981724013467f},
  { -130.500705012420f,    43.2255973783311f},
  { -114.094842552111f,    35.7584993532105f},
  { -145.356185977454f,    33.6469345870906f},
  { -128.973447336866f,    28.2445194108839f},
  { -141.731702622043f,    19.3469890055802f},
  { -150.450437086326f,    -47.7981724013467f},
  { -145.356185977454f,    -33.6469345870906f},
  { -141.731702622043f,    -19.3469890055802f},
  { -130.500705012420f,    -43.2255973783311f},
  { -128.973447336866f,    -28.2445194108839f},
  { -114.094842552111f,    -35.7584993532105f}};
 
/* 3LD geosphere 'ico' [6 0] (362 points) */
const float __geosphere_ico_6_0_dirs_deg[362][2] =
{ { 31.7174744114610f,    0.0f},
  { 148.282525588539f,    0.0f},
  { -148.282525588539f,    0.0f},
  { -31.7174744114610f,    0.0f},
  { 0.0f,    58.2825255885390f},
  { 0.0f,    -58.2825255885390f},
  { 180.0f,    -58.2825255885390f},
  { 180.0f,    58.2825255885390f},
  { 90.0f,    31.7174744114610f},
  { -90.0f,    31.7174744114610f},
  { -90.0f,    -31.7174744114610f},
  { 90.0f,    -31.7174744114610f},
  { 0.0f,    67.6072290710451f},
  { 0.0f,    78.3592768632294f},
  { 0.0f,    90.0f},
  { 180.0f,    78.3592768632294f},
  { 180.0f,    67.6072290710451f},
  { 17.9319334355159f,    59.9665693791348f},
  { 28.3399673707642f,    69.4455573432933f},
  { 58.2825255885390f,    78.1814142633759f},
  { 121.717474411461f,    78.1814142633759f},
  { 151.660032629236f,    69.4455573432933f},
  { 162.068066564484f,    59.9665693791348f},
  { 38.9734473368657f,    58.7297899739513f},
  { 58.2825255885390f,    65.8185857366241f},
  { 90.0f,    69.0948425521107f},
  { 121.717474411461f,    65.8185857366241f},
  { 141.026552663134f,    58.7297899739513f},
  { 58.2825255885390f,    54.0f},
  { 78.3592768632294f,    57.7475579750497f},
  { 101.640723136771f,    57.7475579750497f},
  { 121.717474411461f,    54.0f},
  { 72.8279621494862f,    46.8885380691238f},
  { 90.0f,    48.1896851042214f},
  { 107.172037850514f,    46.8885380691238f},
  { 82.9535936191428f,    39.0716078459179f},
  { 97.0464063808572f,    39.0716078459179f},
  { -17.9319334355159f,    59.9665693791348f},
  { -38.9734473368657f,    58.7297899739513f},
  { -58.2825255885390f,    54.0f},
  { -72.8279621494862f,    46.8885380691238f},
  { -82.9535936191428f,    39.0716078459179f},
  { -28.3399673707642f,    69.4455573432933f},
  { -58.2825255885390f,    65.8185857366241f},
  { -78.3592768632294f,    57.7475579750497f},
  { -90.0f,    48.1896851042214f},
  { -97.0464063808572f,    39.0716078459179f},
  { -58.2825255885390f,    78.1814142633759f},
  { -90.0f,    69.0948425521107f},
  { -101.640723136771f,    57.7475579750497f},
  { -107.172037850514f,    46.8885380691238f},
  { -121.717474411461f,    78.1814142633759f},
  { -121.717474411461f,    65.8185857366241f},
  { -121.717474411461f,    54.0f},
  { -151.660032629236f,    69.4455573432933f},
  { -141.026552663134f,    58.7297899739513f},
  { -162.068066564484f,    59.9665693791348f},
  { 17.9319334355159f,    -59.9665693791348f},
  { 38.9734473368657f,    -58.7297899739513f},
  { 58.2825255885390f,    -54.0f},
  { 72.8279621494862f,    -46.8885380691238f},
  { 82.9535936191428f,    -39.0716078459179f},
  { 0.0f,    -67.6072290710451f},
  { 28.3399673707642f,    -69.4455573432933f},
  { 58.2825255885390f,    -65.8185857366241f},
  { 78.3592768632294f,    -57.7475579750497f},
  { 90.0f,    -48.1896851042214f},
  { 97.0464063808572f,    -39.0716078459179f},
  { 0.0f,    -78.3592768632294f},
  { 58.2825255885390f,    -78.1814142633759f},
  { 90.0f,    -69.0948425521107f},
  { 101.640723136771f,    -57.7475579750497f},
  { 107.172037850514f,    -46.8885380691238f},
  { 0.0f,    -90.0f},
  { 121.717474411461f,    -78.1814142633759f},
  { 121.717474411461f,    -65.8185857366241f},
  { 121.717474411461f,    -54.0f},
  { 180.0f,    -78.3592768632294f},
  { 151.660032629236f,    -69.4455573432933f},
  { 141.026552663134f,    -58.7297899739513f},
  { 180.0f,    -67.6072290710451f},
  { 162.068066564484f,    -59.9665693791348f},
  { -17.9319334355159f,    -59.9665693791348f},
  { -28.3399673707642f,    -69.4455573432933f},
  { -58.2825255885390f,    -78.1814142633759f},
  { -121.717474411461f,    -78.1814142633759f},
  { -151.660032629236f,    -69.4455573432933f},
  { -162.068066564484f,    -59.9665693791348f},
  { -38.9734473368657f,    -58.7297899739513f},
  { -58.2825255885390f,    -65.8185857366241f},
  { -90.0f,    -69.0948425521107f},
  { -121.717474411461f,    -65.8185857366241f},
  { -141.026552663134f,    -58.7297899739513f},
  { -58.2825255885390f,    -54.0f},
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  { -101.640723136771f,    -57.7475579750497f},
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  { -82.9535936191428f,    -39.0716078459179f},
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  { 22.3927709289549f,    0.0f},
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  { -22.3927709289549f,    0.0f},
  { 28.8127609872844f,    8.86454598437525f},
  { 18.2642763775679f,    9.59406822686046f},
  { 6.27780483909150f,    10.0335510226076f},
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  { 0.0f,    20.9051574478893f},
  { -13.2825255885390f,    20.3925183693779f},
  { -25.2736805860404f,    19.0551045548580f},
  { 20.9051574478893f,    30.0000000000000f},
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  { -20.9051574478893f,    30.0000000000000f},
  { 15.4504370863258f,    40.7647476003615f},
  { 0.0f,    41.8103148957786f},
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  { 8.59252164094535f,    50.3983682135674f},
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  { -171.407478359055f,    50.3983682135674f},
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  { 90.0f,    22.3927709289549f},
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  { 79.9071595156824f,    28.4369994004269f},
  { 79.9071595156824f,    18.0f},
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  { 58.2825255885390f,    18.0f},
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  { 46.8095496995643f,    -22.9282785675942f},
  { 33.9705954101743f,    -27.1374399585075f},
  { 36.9382074899021f,    -15.6447696005703f},
  { -24.9857717894179f,    50.3244736173956f},
  { -30.1213952152451f,    39.0760490721854f},
  { -33.9705954101743f,    27.1374399585075f},
  { -36.9382074899021f,    15.6447696005703f},
  { -42.5297913750327f,    47.5637193063793f},
  { -45.0000000000000f,    35.2643896827547f},
  { -46.8095496995643f,    22.9282785675942f},
  { -58.2825255885390f,    42.1814142633759f},
  { -58.2825255885390f,    29.8185857366241f},
  { -70.6909217483267f,    35.3584095083404f},
  { -24.9857717894179f,    -50.3244736173956f},
  { -42.5297913750327f,    -47.5637193063793f},
  { -58.2825255885390f,    -42.1814142633759f},
  { -70.6909217483267f,    -35.3584095083404f},
  { -30.1213952152451f,    -39.0760490721854f},
  { -45.0000000000000f,    -35.2643896827547f},
  { -58.2825255885390f,    -29.8185857366241f},
  { -33.9705954101743f,    -27.1374399585075f},
  { -46.8095496995643f,    -22.9282785675942f},
  { -36.9382074899021f,    -15.6447696005703f},
  { 155.014228210582f,    50.3244736173956f},
  { 149.878604784755f,    39.0760490721854f},
  { 146.029404589826f,    27.1374399585075f},
  { 143.061792510098f,    15.6447696005703f},
  { 137.470208624967f,    47.5637193063793f},
  { 135.0f,    35.2643896827547f},
  { 133.190450300436f,    22.9282785675942f},
  { 121.717474411461f,    42.1814142633759f},
  { 121.717474411461f,    29.8185857366241f},
  { 109.309078251673f,    35.3584095083404f},
  { 155.014228210582f,    -50.3244736173956f},
  { 137.470208624967f,    -47.5637193063793f},
  { 121.717474411461f,    -42.1814142633759f},
  { 109.309078251673f,    -35.3584095083403f},
  { 149.878604784755f,    -39.0760490721854f},
  { 135.0f,    -35.2643896827547f},
  { 121.717474411461f,    -29.8185857366241f},
  { 146.029404589826f,    -27.1374399585075f},
  { 133.190450300436f,    -22.9282785675942f},
  { 143.061792510098f,    -15.6447696005703f},
  { -155.014228210582f,    50.3244736173956f},
  { -137.470208624967f,    47.5637193063793f},
  { -121.717474411461f,    42.1814142633759f},
  { -109.309078251673f,    35.3584095083403f},
  { -149.878604784755f,    39.0760490721854f},
  { -135.0f,    35.2643896827547f},
  { -121.717474411461f,    29.8185857366241f},
  { -146.029404589826f,    27.1374399585075f},
  { -133.190450300436f,    22.9282785675942f},
  { -143.061792510098f,    15.6447696005703f},
  { -155.014228210582f,    -50.3244736173956f},
  { -149.878604784755f,    -39.0760490721854f},
  { -146.029404589826f,    -27.1374399585075f},
  { -143.061792510098f,    -15.6447696005703f},
  { -137.470208624967f,    -47.5637193063793f},
  { -135.0f,    -35.2643896827547f},
  { -133.190450300436f,    -22.9282785675942f},
  { -121.717474411461f,    -42.1814142633759f},
  { -121.717474411461f,    -29.8185857366241f},
  { -109.309078251673f,    -35.3584095083404f}};
 
/* 3LD geosphere 'ico' [7 0] (492 points) */
const float __geosphere_ico_7_0_dirs_deg[492][2] =
{ { 31.7174744114610f,    0.0f},
  { 148.282525588539f,    0.0f},
  { -148.282525588539f,    0.0f},
  { -31.7174744114610f,    0.0f},
  { 0.0f,    58.2825255885390f},
  { 0.0f,    -58.2825255885390f},
  { 180.0f,    -58.2825255885390f},
  { 180.0f,    58.2825255885390f},
  { 90.0f,    31.7174744114610f},
  { -90.0f,    31.7174744114610f},
  { -90.0f,    -31.7174744114610f},
  { 90.0f,    -31.7174744114610f},
  { 0.0f,    66.1808024884231f},
  { 0.0f,    75.1646413480039f},
  { 0.0f,    84.9544063480986f},
  { 180.0f,    84.9544063480986f},
  { 180.0f,    75.1646413480039f},
  { 180.0f,    66.1808024884231f},
  { 15.0920752881032f,    59.8719245592249f},
  { 22.0237505161462f,    68.0530702426802f},
  { 38.9734473368657f,    76.4911891305542f},
  { 90.0000000000000f,    81.4074783590547f},
  { 141.026552663134f,    76.4911891305542f},
  { 157.976249483854f,    68.0530702426802f},
  { 164.907924711897f,    59.8719245592249f},
  { 32.9114931857064f,    59.4482400957790f},
  { 47.1679114977869f,    66.3788444575833f},
  { 72.8279621494862f,    71.4441996352265f},
  { 107.172037850514f,    71.4441996352265f},
  { 132.832088502213f,    66.3788444575833f},
  { 147.088506814294f,    59.4482400957790f},
  { 50.5099309427673f,    56.4143320128269f},
  { 67.6072290710451f,    61.0023561147386f},
  { 90.0f,    62.8666219591469f},
  { 112.392770928955f,    61.0023561147386f},
  { 129.490069057233f,    56.4143320128269f},
  { 65.1310748815380f,    51.1421142488325f},
  { 81.2167693990410f,    53.5115270803982f},
  { 98.7832306009590f,    53.5115270803982f},
  { 114.868925118462f,    51.1421142488325f},
  { 76.1141128518623f,    44.6623463365959f},
  { 90.0f,    45.5120052212781f},
  { 103.885887148138f,    44.6623463365959f},
  { 84.1189512527134f,    37.9745512724670f},
  { 95.8810487472866f,    37.9745512724670f},
  { -15.0920752881032f,    59.8719245592249f},
  { -32.9114931857064f,    59.4482400957790f},
  { -50.5099309427673f,    56.4143320128269f},
  { -65.1310748815380f,    51.1421142488325f},
  { -76.1141128518623f,    44.6623463365959f},
  { -84.1189512527134f,    37.9745512724670f},
  { -22.0237505161462f,    68.0530702426802f},
  { -47.1679114977869f,    66.3788444575833f},
  { -67.6072290710451f,    61.0023561147386f},
  { -81.2167693990410f,    53.5115270803982f},
  { -90.0000000000000f,    45.5120052212781f},
  { -95.8810487472866f,    37.9745512724671f},
  { -38.9734473368657f,    76.4911891305542f},
  { -72.8279621494862f,    71.4441996352265f},
  { -90.0f,    62.8666219591469f},
  { -98.7832306009590f,    53.5115270803982f},
  { -103.885887148138f,    44.6623463365959f},
  { -90.0000000000000f,    81.4074783590547f},
  { -107.172037850514f,    71.4441996352265f},
  { -112.392770928955f,    61.0023561147386f},
  { -114.868925118462f,    51.1421142488325f},
  { -141.026552663134f,    76.4911891305542f},
  { -132.832088502213f,    66.3788444575833f},
  { -129.490069057233f,    56.4143320128269f},
  { -157.976249483854f,    68.0530702426802f},
  { -147.088506814294f,    59.4482400957790f},
  { -164.907924711897f,    59.8719245592249f},
  { 15.0920752881032f,    -59.8719245592249f},
  { 32.9114931857064f,    -59.4482400957790f},
  { 50.5099309427673f,    -56.4143320128269f},
  { 65.1310748815380f,    -51.1421142488325f},
  { 76.1141128518623f,    -44.6623463365959f},
  { 84.1189512527134f,    -37.9745512724670f},
  { 0.0f,    -66.1808024884231f},
  { 22.0237505161462f,    -68.0530702426802f},
  { 47.1679114977869f,    -66.3788444575833f},
  { 67.6072290710451f,    -61.0023561147386f},
  { 81.2167693990410f,    -53.5115270803982f},
  { 90.0000000000000f,    -45.5120052212781f},
  { 95.8810487472866f,    -37.9745512724671f},
  { 0.0f,    -75.1646413480039f},
  { 38.9734473368657f,    -76.4911891305542f},
  { 72.8279621494862f,    -71.4441996352265f},
  { 90.0f,    -62.8666219591469f},
  { 98.7832306009590f,    -53.5115270803982f},
  { 103.885887148138f,    -44.6623463365959f},
  { 0.0f,    -84.9544063480986f},
  { 90.0000000000000f,    -81.4074783590547f},
  { 107.172037850514f,    -71.4441996352265f},
  { 112.392770928955f,    -61.0023561147386f},
  { 114.868925118462f,    -51.1421142488325f},
  { 180.0f,    -84.9544063480986f},
  { 141.026552663134f,    -76.4911891305542f},
  { 132.832088502213f,    -66.3788444575833f},
  { 129.490069057233f,    -56.4143320128269f},
  { 180.0f,    -75.1646413480039f},
  { 157.976249483854f,    -68.0530702426802f},
  { 147.088506814294f,    -59.4482400957790f},
  { 180.0f,    -66.1808024884231f},
  { 164.907924711897f,    -59.8719245592249f},
  { -15.0920752881032f,    -59.8719245592249f},
  { -22.0237505161462f,    -68.0530702426802f},
  { -38.9734473368657f,    -76.4911891305542f},
  { -90.0000000000000f,    -81.4074783590547f},
  { -141.026552663134f,    -76.4911891305542f},
  { -157.976249483854f,    -68.0530702426802f},
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  { -32.9114931857064f,    -59.4482400957790f},
  { -47.1679114977869f,    -66.3788444575833f},
  { -72.8279621494862f,    -71.4441996352265f},
  { -107.172037850514f,    -71.4441996352265f},
  { -132.832088502213f,    -66.3788444575833f},
  { -147.088506814294f,    -59.4482400957790f},
  { -50.5099309427673f,    -56.4143320128269f},
  { -67.6072290710451f,    -61.0023561147386f},
  { -90.0f,    -62.8666219591469f},
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  { -114.868925118462f,    -51.1421142488325f},
  { -76.1141128518623f,    -44.6623463365959f},
  { -90.0f,    -45.5120052212781f},
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  { -16.5582178401620f,    17.0882173737518f},
  { -26.3598778094528f,    16.0329525274240f},
  { 22.8939075042604f,    25.2716662118425f},
  { 11.9226312702234f,    26.6294653632014f},
  { 0.0f,    27.1333780408531f},
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  { 18.7177168090702f,    34.6954547665617f},
  { 6.44379382542064f,    35.9930793767210f},
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  { -18.7177168090702f,    34.6954547665617f},
  { 13.6491845224847f,    43.6677528316015f},
  { 0.0f,    44.4879947787219f},
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  { 7.47831395519902f,    51.6407658043736f},
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  { 29.2626971786928f,    -7.50942039010128f},
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  { 10.5793931769549f,    -8.44858701261369f},
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  { 0.0f,    -27.1333780408531f},
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  { -156.180802488423f,    0.0f},
  { -165.164641348004f,    0.0f},
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  { -159.517058553905f,    8.05663962251492f},
  { -169.420606823045f,    8.44858701261369f},
  { -180.0f,    8.59252164094535f},
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  { -157.106092495740f,    25.2716662118425f},
  { -168.077368729777f,    26.6294653632014f},
  { 180.0f,    27.1333780408531f},
  { 168.077368729777f,    26.6294653632014f},
  { 157.106092495740f,    25.2716662118425f},
  { -161.282283190930f,    34.6954547665617f},
  { -173.556206174579f,    35.9930793767210f},
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  { -166.350815477515f,    43.6677528316015f},
  { 180.0f,    44.4879947787219f},
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  { -172.521686044801f,    51.6407658043736f},
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  { -150.737302821307f,    -7.50942039010128f},
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  { 90.0f,    23.8191975115769f},
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  { 81.4074783590547f,    28.9877234630627f},
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  { 81.4074783590547f,    10.4632857609175f},
  { 81.4074783590547f,    3.91037549404927e-15f},
  { 81.4074783590547f,    -10.4632857609175f},
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  { 72.2181794238810f,    25.2606763729821f},
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  { 72.2181794238810f,    -15.8076162308333f},
  { 72.2181794238810f,    -25.2606763729821f},
  { 62.8666219591469f,    20.5970703451119f},
  { 62.8666219591469f,    10.6422621988362f},
  { 62.8666219591469f,    0.0f},
  { 62.8666219591469f,    -10.6422621988362f},
  { 62.8666219591469f,    -20.5970703451119f},
  { 53.8340928444730f,    15.2983539399373f},
  { 53.8340928444730f,    5.20978847514459f},
  { 53.8340928444730f,    -5.20978847514459f},
  { 53.8340928444730f,    -15.2983539399373f},
  { 45.5120052212781f,    9.82822484687696f},
  { 45.5120052212781f,    0.0f},
  { 45.5120052212781f,    -9.82822484687696f},
  { 38.1213002554066f,    4.63284787319209f},
  { 38.1213002554066f,    -4.63284787319209f},
  { 98.5925216409454f,    28.9877234630627f},
  { 107.781820576119f,    25.2606763729821f},
  { 117.133378040853f,    20.5970703451119f},
  { 126.165907155527f,    15.2983539399373f},
  { 134.487994778722f,    9.82822484687696f},
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  { 117.133378040853f,    0.0f},
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  { 107.781820576119f,    -15.8076162308333f},
  { 117.133378040853f,    -20.5970703451119f},
  { 98.5925216409454f,    -20.2718429567436f},
  { 107.781820576119f,    -25.2606763729821f},
  { 98.5925216409454f,    -28.9877234630627f},
  { -81.4074783590547f,    28.9877234630627f},
  { -72.2181794238810f,    25.2606763729821f},
  { -62.8666219591469f,    20.5970703451119f},
  { -53.8340928444730f,    15.2983539399373f},
  { -45.5120052212781f,    9.82822484687696f},
  { -38.1213002554066f,    4.63284787319209f},
  { -90.0f,    23.8191975115769f},
  { -81.4074783590547f,    20.2718429567436f},
  { -72.2181794238810f,    15.8076162308333f},
  { -62.8666219591469f,    10.6422621988362f},
  { -53.8340928444730f,    5.20978847514459f},
  { -45.5120052212781f,    -3.66816416523558e-15f},
  { -38.1213002554066f,    -4.63284787319209f},
  { -90.0f,    14.8353586519961f},
  { -81.4074783590547f,    10.4632857609175f},
  { -72.2181794238810f,    5.39113258470827f},
  { -62.8666219591469f,    0.0f},
  { -53.8340928444730f,    -5.20978847514458f},
  { -45.5120052212781f,    -9.82822484687696f},
  { -90.0f,    5.04559365190141f},
  { -81.4074783590547f,    -1.95518774702464e-15f},
  { -72.2181794238810f,    -5.39113258470827f},
  { -62.8666219591469f,    -10.6422621988362f},
  { -53.8340928444730f,    -15.2983539399373f},
  { -90.0f,    -5.04559365190141f},
  { -81.4074783590547f,    -10.4632857609175f},
  { -72.2181794238810f,    -15.8076162308333f},
  { -62.8666219591469f,    -20.5970703451119f},
  { -90.0f,    -14.8353586519961f},
  { -81.4074783590547f,    -20.2718429567436f},
  { -72.2181794238810f,    -25.2606763729821f},
  { -90.0f,    -23.8191975115769f},
  { -81.4074783590547f,    -28.9877234630627f},
  { -98.5925216409454f,    28.9877234630627f},
  { -98.5925216409454f,    20.2718429567436f},
  { -98.5925216409454f,    10.4632857609175f},
  { -98.5925216409454f,    3.91037549404927e-15f},
  { -98.5925216409454f,    -10.4632857609175f},
  { -98.5925216409454f,    -20.2718429567436f},
  { -98.5925216409454f,    -28.9877234630627f},
  { -107.781820576119f,    25.2606763729821f},
  { -107.781820576119f,    15.8076162308333f},
  { -107.781820576119f,    5.39113258470827f},
  { -107.781820576119f,    -5.39113258470827f},
  { -107.781820576119f,    -15.8076162308333f},
  { -107.781820576119f,    -25.2606763729821f},
  { -117.133378040853f,    20.5970703451119f},
  { -117.133378040853f,    10.6422621988362f},
  { -117.133378040853f,    0.0f},
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  { -126.165907155527f,    15.2983539399373f},
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  { -126.165907155527f,    -5.20978847514459f},
  { -126.165907155527f,    -15.2983539399373f},
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  { -134.487994778722f,    0.0f},
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  { -141.878699744593f,    4.63284787319209f},
  { -141.878699744593f,    -4.63284787319209f},
  { 73.9332208850461f,    34.9768443320308f},
  { 63.4349488229220f,    30.6726725373555f},
  { 53.3007747995101f,    25.2406273115173f},
  { 44.0804766102169f,    19.1794139209880f},
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  { 42.2968675884159f,    29.4688797542767f},
  { 33.5491126061725f,    22.6217951428160f},
  { 51.7317026220431f,    46.4882636786595f},
  { 40.0182492109711f,    40.0886354813392f},
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  { -37.0167508575842f,    -50.2904398912844f},
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  { -26.5650511770780f,    -42.7257778636242f},
  { -40.0182492109711f,    -40.0886354813392f},
  { -52.6226318593503f,    -35.8669489234169f},
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  { 149.545436560947f,    32.7215661485233f},
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  { 139.981750789029f,    40.0886354813392f},
  { 137.703132411584f,    29.4688797542767f},
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  { 106.066779114954f,    34.9768443320308f},
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  { 115.836425664174f,    -41.0756272443228f},
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  { 153.434948822922f,    -42.7257778636242f},
  { 139.981750789029f,    -40.0886354813392f},
  { 127.377368140650f,    -35.8669489234169f},
  { 116.565051177078f,    -30.6726725373555f},
  { 149.545436560947f,    -32.7215661485233f},
  { 137.703132411584f,    -29.4688797542767f},
  { 126.699225200490f,    -25.2406273115173f},
  { 146.450887393828f,    -22.6217951428160f},
  { 135.919523389783f,    -19.1794139209880f},
  { 143.943774079151f,    -13.1070197584612f},
  { -158.416699611951f,    51.9411964822148f},
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  { -128.268297377957f,    46.4882636786595f},
  { -115.836425664174f,    41.0756272443228f},
  { -106.066779114954f,    34.9768443320308f},
  { -153.434948822922f,    42.7257778636242f},
  { -139.981750789029f,    40.0886354813392f},
  { -127.377368140650f,    35.8669489234169f},
  { -116.565051177078f,    30.6726725373555f},
  { -149.545436560947f,    32.7215661485233f},
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  { -126.699225200490f,    25.2406273115173f},
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  { -135.919523389783f,    19.1794139209880f},
  { -143.943774079151f,    13.1070197584612f},
  { -158.416699611951f,    -51.9411964822148f},
  { -153.434948822922f,    -42.7257778636242f},
  { -149.545436560947f,    -32.7215661485233f},
  { -146.450887393828f,    -22.6217951428160f},
  { -143.943774079151f,    -13.1070197584612f},
  { -142.983249142416f,    -50.2904398912844f},
  { -139.981750789029f,    -40.0886354813392f},
  { -137.703132411584f,    -29.4688797542767f},
  { -135.919523389783f,    -19.1794139209880f},
  { -128.268297377957f,    -46.4882636786595f},
  { -127.377368140650f,    -35.8669489234169f},
  { -126.699225200490f,    -25.2406273115173f},
  { -115.836425664174f,    -41.0756272443228f},
  { -116.565051177078f,    -30.6726725373555f},
  { -106.066779114954f,    -34.9768443320308f}};
 
/* 3LD geosphere 'ico' [8 0] (642 points) */
const float __geosphere_ico_8_0_dirs_deg[642][2] =
{ { 31.7174744114610f,    0.0f},
  { 148.282525588539f,    0.0f},
  { -148.282525588539f,    0.0f},
  { -31.7174744114610f,    0.0f},
  { 0.0f,    58.2825255885390f},
  { 0.0f,    -58.2825255885390f},
  { 180.0f,    -58.2825255885390f},
  { 180.0f,    58.2825255885390f},
  { 90.0f,    31.7174744114610f},
  { -90.0f,    31.7174744114610f},
  { -90.0f,    -31.7174744114610f},
  { 90.0f,    -31.7174744114610f},
  { 0.0f,    65.1310748815380f},
  { 0.0f,    72.8279621494862f},
  { 0.0f,    81.2167693990410f},
  { 0.0f,    90.0f},
  { 180.0f,    81.2167693990410f},
  { 180.0f,    72.8279621494862f},
  { 180.0f,    65.1310748815380f},
  { 13.0152040462228f,    59.7634611728920f},
  { 17.9319334355159f,    66.9090449293358f},
  { 28.3399673707642f,    74.5425010655038f},
  { 58.2825255885390f,    81.2276448816065f},
  { 121.717474411461f,    81.2276448816065f},
  { 151.660032629236f,    74.5425010655038f},
  { 162.068066564484f,    66.9090449293358f},
  { 166.984795953777f,    59.7634611728920f},
  { 28.3399673707642f,    59.7900946927798f},
  { 38.9734473368657f,    66.2771675744593f},
  { 58.2825255885390f,    72.0f},
  { 90.0f,    74.5495629136742f},
  { 121.717474411461f,    72.0f},
  { 141.026552663134f,    66.2771675744593f},
  { 151.660032629236f,    59.7900946927798f},
  { 44.1517511327961f,    57.8562154800787f},
  { 58.2825255885390f,    62.7723551183935f},
  { 78.3592768632294f,    65.9208196976405f},
  { 101.640723136771f,    65.9208196976405f},
  { 121.717474411461f,    62.7723551183935f},
  { 135.848248867204f,    57.8562154800787f},
  { 58.2825255885390f,    54.0f},
  { 72.8279621494862f,    57.1023923174897f},
  { 90.0f,    58.2825255885390f},
  { 107.172037850514f,    57.1023923174897f},
  { 121.717474411461f,    54.0f},
  { 69.6541923856616f,    48.7938239499718f},
  { 82.9535936191428f,    50.4009770857117f},
  { 97.0464063808572f,    50.4009770857117f},
  { 110.345807614338f,    48.7938239499718f},
  { 78.3592768632294f,    42.9780676586279f},
  { 90.0f,    43.5723495188822f},
  { 101.640723136771f,    42.9780676586279f},
  { 84.9544063480986f,    37.1600422047896f},
  { 95.0455936519014f,    37.1600422047896f},
  { -13.0152040462228f,    59.7634611728920f},
  { -28.3399673707642f,    59.7900946927798f},
  { -44.1517511327961f,    57.8562154800787f},
  { -58.2825255885390f,    54.0f},
  { -69.6541923856616f,    48.7938239499718f},
  { -78.3592768632294f,    42.9780676586279f},
  { -84.9544063480986f,    37.1600422047896f},
  { -17.9319334355159f,    66.9090449293358f},
  { -38.9734473368657f,    66.2771675744593f},
  { -58.2825255885390f,    62.7723551183935f},
  { -72.8279621494862f,    57.1023923174897f},
  { -82.9535936191428f,    50.4009770857117f},
  { -90.0f,    43.5723495188822f},
  { -95.0455936519014f,    37.1600422047896f},
  { -28.3399673707642f,    74.5425010655038f},
  { -58.2825255885390f,    72.0f},
  { -78.3592768632294f,    65.9208196976405f},
  { -90.0f,    58.2825255885390f},
  { -97.0464063808572f,    50.4009770857117f},
  { -101.640723136771f,    42.9780676586279f},
  { -58.2825255885390f,    81.2276448816065f},
  { -90.0000000000000f,    74.5495629136742f},
  { -101.640723136771f,    65.9208196976405f},
  { -107.172037850514f,    57.1023923174897f},
  { -110.345807614338f,    48.7938239499718f},
  { -121.717474411461f,    81.2276448816065f},
  { -121.717474411461f,    72.0f},
  { -121.717474411461f,    62.7723551183935f},
  { -121.717474411461f,    54.0f},
  { -151.660032629236f,    74.5425010655038f},
  { -141.026552663134f,    66.2771675744593f},
  { -135.848248867204f,    57.8562154800787f},
  { -162.068066564484f,    66.9090449293358f},
  { -151.660032629236f,    59.7900946927798f},
  { -166.984795953777f,    59.7634611728920f},
  { 13.0152040462228f,    -59.7634611728920f},
  { 28.3399673707642f,    -59.7900946927798f},
  { 44.1517511327961f,    -57.8562154800787f},
  { 58.2825255885390f,    -54.0f},
  { 69.6541923856616f,    -48.7938239499718f},
  { 78.3592768632294f,    -42.9780676586279f},
  { 84.9544063480986f,    -37.1600422047896f},
  { 0.0f,    -65.1310748815380f},
  { 17.9319334355159f,    -66.9090449293358f},
  { 38.9734473368657f,    -66.2771675744593f},
  { 58.2825255885390f,    -62.7723551183935f},
  { 72.8279621494862f,    -57.1023923174897f},
  { 82.9535936191428f,    -50.4009770857117f},
  { 90.0f,    -43.5723495188822f},
  { 95.0455936519014f,    -37.1600422047896f},
  { 0.0f,    -72.8279621494862f},
  { 28.3399673707642f,    -74.5425010655038f},
  { 58.2825255885390f,    -72.0f},
  { 78.3592768632294f,    -65.9208196976405f},
  { 90.0f,    -58.2825255885390f},
  { 97.0464063808572f,    -50.4009770857117f},
  { 101.640723136771f,    -42.9780676586279f},
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  { -131.110487738025f,    -30.8889289128016f},
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  { -121.717474411461f,    -36.0f},
  { -121.717474411461f,    -26.7723551183935f},
  { -111.703351896392f,    -40.0910997872291f},
  { -112.773700332310f,    -31.1637336664207f},
  { -103.738656574656f,    -34.6470309014331f}};
 
/* 3LD geosphere 'ico' [9 0] (812 points) */
const float __geosphere_ico_9_0_dirs_deg[812][2] =
{ { 31.7174744114610f,    0.0f},
  { 148.282525588539f,    0.0f},
  { -148.282525588539f,    0.0f},
  { -31.7174744114610f,    0.0f},
  { 0.0f,    58.2825255885390f},
  { 0.0f,    -58.2825255885390f},
  { 180.0f,    -58.2825255885390f},
  { 180.0f,    58.2825255885390f},
  { 90.0f,    31.7174744114610f},
  { -90.0f,    31.7174744114610f},
  { -90.0f,    -31.7174744114610f},
  { 90.0f,    -31.7174744114610f},
  { 0.0f,    64.3267273510545f},
  { 0.0f,    71.0499775117081f},
  { 0.0f,    78.3592768632294f},
  { 0.0f,    86.0716405780585f},
  { 180.0f,    86.0716405780585f},
  { 180.0f,    78.3592768632294f},
  { 180.0f,    71.0499775117081f},
  { 180.0f,    64.3267273510545f},
  { 11.4340697442537f,    59.6583225872452f},
  { 15.0920752881032f,    65.9795958419257f},
  { 22.0237505161462f,    72.8060416440631f},
  { 38.9734473368657f,    79.5471366108243f},
  { 90.0f,    83.3812412279501f},
  { 141.026552663134f,    79.5471366108243f},
  { 157.976249483854f,    72.8060416440631f},
  { 164.907924711897f,    65.9795958419257f},
  { 168.565930255746f,    59.6583225872452f},
  { 24.8108847601265f,    59.9422780929273f},
  { 32.9114931857064f,    65.9188666651293f},
  { 47.1679114977869f,    71.6787159647749f},
  { 72.8279621494862f,    75.7394148284850f},
  { 107.172037850514f,    75.7394148284850f},
  { 132.832088502213f,    71.6787159647749f},
  { 147.088506814294f,    65.9188666651293f},
  { 155.189115239873f,    59.9422780929273f},
  { 38.9734473368657f,    58.7297899739513f},
  { 50.5099309427673f,    63.6671378427701f},
  { 67.6072290710451f,    67.5536234094196f},
  { 90.0000000000000f,    69.0948425521107f},
  { 112.392770928955f,    67.5536234094196f},
  { 129.490069057233f,    63.6671378427701f},
  { 141.026552663134f,    58.7297899739513f},
  { 52.3123893000598f,    55.9231386404846f},
  { 65.1310748815380f,    59.4579173207107f},
  { 81.2167693990410f,    61.5567324441311f},
  { 98.7832306009590f,    61.5567324441311f},
  { 114.868925118462f,    59.4579173207107f},
  { 127.687610699940f,    55.9231386404846f},
  { 63.6909565444517f,    51.8082310918389f},
  { 76.1141128518623f,    54.0041745863830f},
  { 90.0f,    54.8084438762714f},
  { 103.885887148138f,    54.0041745863830f},
  { 116.309043455548f,    51.8082310918389f},
  { 72.8279621494862f,    46.8885380691238f},
  { 84.1189512527134f,    48.0393989970589f},
  { 95.8810487472866f,    48.0393989970589f},
  { 107.172037850514f,    46.8885380691238f},
  { 79.9858774849308f,    41.6684303531219f},
  { 90.0f,    42.1056437002381f},
  { 100.014122515069f,    41.6684303531219f},
  { 85.5824320004692f,    36.5320305814123f},
  { 94.4175679995308f,    36.5320305814123f},
  { -11.4340697442537f,    59.6583225872452f},
  { -24.8108847601265f,    59.9422780929273f},
  { -38.9734473368657f,    58.7297899739513f},
  { -52.3123893000598f,    55.9231386404846f},
  { -63.6909565444517f,    51.8082310918389f},
  { -72.8279621494862f,    46.8885380691238f},
  { -79.9858774849308f,    41.6684303531219f},
  { -85.5824320004692f,    36.5320305814123f},
  { -15.0920752881032f,    65.9795958419257f},
  { -32.9114931857064f,    65.9188666651293f},
  { -50.5099309427673f,    63.6671378427701f},
  { -65.1310748815380f,    59.4579173207107f},
  { -76.1141128518623f,    54.0041745863830f},
  { -84.1189512527134f,    48.0393989970589f},
  { -90.0f,    42.1056437002381f},
  { -94.4175679995308f,    36.5320305814124f},
  { -22.0237505161462f,    72.8060416440631f},
  { -47.1679114977869f,    71.6787159647749f},
  { -67.6072290710451f,    67.5536234094196f},
  { -81.2167693990410f,    61.5567324441311f},
  { -90.0f,    54.8084438762714f},
  { -95.8810487472866f,    48.0393989970589f},
  { -100.014122515069f,    41.6684303531219f},
  { -38.9734473368657f,    79.5471366108243f},
  { -72.8279621494862f,    75.7394148284850f},
  { -90.0f,    69.0948425521107f},
  { -98.7832306009590f,    61.5567324441311f},
  { -103.885887148138f,    54.0041745863831f},
  { -107.172037850514f,    46.8885380691238f},
  { -90.0f,    83.3812412279501f},
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  { -112.392770928955f,    67.5536234094196f},
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  { -141.026552663134f,    58.7297899739513f},
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  { 11.4340697442537f,    -59.6583225872452f},
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  { 38.9734473368657f,    -58.7297899739513f},
  { 52.3123893000598f,    -55.9231386404846f},
  { 63.6909565444517f,    -51.8082310918389f},
  { 72.8279621494862f,    -46.8885380691238f},
  { 79.9858774849308f,    -41.6684303531219f},
  { 85.5824320004692f,    -36.5320305814123f},
  { 0.0f,    -64.3267273510545f},
  { 15.0920752881032f,    -65.9795958419257f},
  { 32.9114931857064f,    -65.9188666651293f},
  { 50.5099309427673f,    -63.6671378427701f},
  { 65.1310748815380f,    -59.4579173207107f},
  { 76.1141128518623f,    -54.0041745863830f},
  { 84.1189512527134f,    -48.0393989970589f},
  { 90.0f,    -42.1056437002381f},
  { 94.4175679995308f,    -36.5320305814124f},
  { 0.0f,    -71.0499775117081f},
  { 22.0237505161462f,    -72.8060416440631f},
  { 47.1679114977869f,    -71.6787159647749f},
  { 67.6072290710451f,    -67.5536234094196f},
  { 81.2167693990410f,    -61.5567324441311f},
  { 90.0f,    -54.8084438762714f},
  { 95.8810487472866f,    -48.0393989970589f},
  { 100.014122515069f,    -41.6684303531219f},
  { 0.0f,    -78.3592768632294f},
  { 38.9734473368657f,    -79.5471366108243f},
  { 72.8279621494862f,    -75.7394148284850f},
  { 90.0f,    -69.0948425521107f},
  { 98.7832306009590f,    -61.5567324441311f},
  { 103.885887148138f,    -54.0041745863831f},
  { 107.172037850514f,    -46.8885380691238f},
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  { -135.0f,    -35.2643896827547f},
  { -133.737089027592f,    -26.9706688639076f},
  { -132.690785960849f,    -19.0068859665187f},
  { -126.938207489902f,    -48.2445277172896f},
  { -126.355594534215f,    -40.0860717757720f},
  { -125.889754659584f,    -31.7532340351390f},
  { -125.508825256229f,    -23.5910973678578f},
  { -116.931710111024f,    -44.0232126088419f},
  { -117.426045898242f,    -35.9235381066138f},
  { -117.827962149486f,    -27.8222160665198f},
  { -108.668823371438f,    -39.2536542921232f},
  { -109.890296064862f,    -31.4600994569254f},
  { -101.991154997501f,    -34.3684513220687f}};
 
/* 3LD geosphere 'ico' [10 0] (1002 points) */
const float __geosphere_ico_10_0_dirs_deg[1002][2] =
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  { 148.282525588539f,    0.0f},
  { -148.282525588539f,    0.0f},
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  { 0.0f,    58.2825255885390f},
  { 0.0f,    -58.2825255885390f},
  { 180.0f,    -58.2825255885390f},
  { 180.0f,    58.2825255885390f},
  { 90.0f,    31.7174744114610f},
  { -90.0f,    31.7174744114610f},
  { -90.0f,    -31.7174744114610f},
  { 90.0f,    -31.7174744114610f},
  { 0.0f,    63.6909565444517f},
  { 0.0f,    69.6541923856616f},
  { 0.0f,    76.1141128518623f},
  { 0.0f,    82.9535936191428f},
  { 0.0f,    90.0f},
  { 180.0f,    82.9535936191428f},
  { 180.0f,    76.1141128518623f},
  { 180.0f,    69.6541923856616f},
  { 180.0f,    63.6909565444517f},
  { 10.1918500362761f,    59.5618368610333f},
  { 13.0152040462228f,    65.2188912720402f},
  { 17.9319334355159f,    71.3405195718550f},
  { 28.3399673707642f,    77.6459130495745f},
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  { 166.984795953777f,    65.2188912720402f},
  { 169.808149963724f,    59.5618368610333f},
  { 22.0237505161462f,    59.9952713133382f},
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  { 38.9734473368657f,    71.0021166134344f},
  { 58.2825255885390f,    75.7180776303631f},
  { 90.0f,    77.7816801337513f},
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  { 90.0f,    64.7263194139596f},
  { 107.172037850514f,    63.7030502822517f},
  { 121.717474411461f,    60.9684505330286f},
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  { 58.2825255885390f,    54.0f},
  { 69.6541923856616f,    56.6088055804906f},
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  { 78.3592768632294f,    51.5245159887128f},
  { 90.0f,    52.1031151288303f},
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  { 75.1646413480039f,    45.3337202344714f},
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  { 95.0455936519014f,    46.1933976926144f},
  { 104.835358651996f,    45.3337202344714f},
  { 81.2167693990410f,    40.6247965576687f},
  { 90.0f,    40.9590912848605f},
  { 98.7832306009590f,    40.6247965576687f},
  { 86.0716405780585f,    36.0333403752908f},
  { 93.9283594219415f,    36.0333403752908f},
  { -10.1918500362761f,    59.5618368610333f},
  { -22.0237505161462f,    59.9952713133382f},
  { -34.7391081893039f,    59.2643719580340f},
  { -47.1679114977868f,    57.2262493118836f},
  { -58.2825255885390f,    54.0f},
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  { -13.0152040462228f,    65.2188912720402f},
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  { -69.6541923856616f,    56.6088055804906f},
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  { -90.0f,    40.9590912848605f},
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  { -141.731702622043f,    -19.3469890055802f},
  { -140.292769124761f,    -12.7247006938203f},
  { -142.459411033721f,    -52.9103051134963f},
  { -140.232582826810f,    -45.9856701791279f},
  { -138.425114566662f,    -38.6705372603619f},
  { -136.931510665258f,    -31.2052664566532f},
  { -135.678142940160f,    -23.8529889684413f},
  { -134.612322817293f,    -16.8503785613218f},
  { -131.531153811135f,    -50.4572066397107f},
  { -130.500705012420f,    -43.2255973783311f},
  { -129.664830160504f,    -35.7374493804082f},
  { -128.973447336866f,    -28.2445194108839f},
  { -128.392229523677f,    -20.9980381353659f},
  { -121.717474411461f,    -47.0315494669714f},
  { -121.717474411461f,    -39.7180776303631f},
  { -121.717474411461f,    -32.2819223696369f},
  { -121.717474411461f,    -24.9684505330286f},
  { -113.328667161906f,    -42.9461472577416f},
  { -114.094842552111f,    -35.7584993532105f},
  { -114.733412982366f,    -28.5668020560704f},
  { -106.358175687714f,    -38.5483024802721f},
  { -107.634120869186f,    -31.6458891485011f},
  { -100.633479966101f,    -34.1334810267585f}};
 
/* 3LD geosphere 'ico' [11 0] (1212 points) */
const float __geosphere_ico_11_0_dirs_deg[1212][2] =
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  { -148.282525588539f,    0.0f},
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  { 0.0f,    58.2825255885390f},
  { 0.0f,    -58.2825255885390f},
  { 180.0f,    -58.2825255885390f},
  { 180.0f,    58.2825255885390f},
  { 90.0f,    31.7174744114610f},
  { -90.0f,    31.7174744114610f},
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  { 90.0f,    -31.7174744114610f},
  { 0.0f,    63.1759109378142f},
  { 0.0f,    68.5305657000874f},
  { 0.0f,    74.3086441830498f},
  { 0.0f,    80.4324561201698f},
  { 0.0f,    86.7842228465557f},
  { 180.0f,    86.7842228465557f},
  { 180.0f,    80.4324561201698f},
  { 180.0f,    74.3086441830498f},
  { 180.0f,    68.5305657000874f},
  { 180.0f,    63.1759109378142f},
  { 9.19099647608508f,    59.4750930157754f},
  { 11.4340697442537f,    64.5886747619424f},
  { 15.0920752881032f,    70.1143173072657f},
  { 22.0237505161462f,    75.9016975056681f},
  { 38.9734473368657f,    81.4839022669666f},
  { 90.0f,    84.6197878514433f},
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  { 157.976249483854f,    75.9016975056681f},
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  { 52.3123893000598f,    61.9142772940601f},
  { 65.1310748815380f,    65.0403053382520f},
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  { 98.7832306009590f,    66.8628767649577f},
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  { 63.6909565444517f,    58.4665560721094f},
  { 76.1141128518623f,    60.4639637602226f},
  { 90.0f,    61.1872390127156f},
  { 103.885887148138f,    60.4639637602226f},
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  { 126.562139238749f,    55.5963831147141f},
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  { 72.8279621494862f,    54.2026444179102f},
  { 84.1189512527134f,    55.2915500640743f},
  { 95.8810487472866f,    55.2915500640743f},
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  { 70.5487009486867f,    48.2796684813088f},
  { 79.9858774849308f,    49.5118734071249f},
  { 90.0f,    49.9457026117864f},
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  { 109.451299051313f,    48.2796684813088f},
  { 76.9513489599765f,    44.0504703995995f},
  { 85.5824320004692f,    44.7145105417809f},
  { 94.4175679995308f,    44.7145105417809f},
  { 103.048651040024f,    44.0504703995995f},
  { 82.1798710590254f,    39.7754154552892f},
  { 90.0f,    40.0388650148264f},
  { 97.8201289409746f,    39.7754154552892f},
  { 86.4634243465556f,    35.6279040820967f},
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  { -9.19099647608508f,    59.4750930157754f},
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  { -31.2478160930689f,    59.5919152427842f},
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  { -124.777164437380f,    -22.5514345501505f},
  { -117.683644245335f,    -45.8854719044003f},
  { -118.040826793942f,    -39.2909610056656f},
  { -118.339967370764f,    -32.6059411168087f},
  { -118.594137539691f,    -26.0099241206311f},
  { -110.538498513944f,    -42.0051882309740f},
  { -111.450567816686f,    -35.5613266886593f},
  { -112.226299667690f,    -29.1116228424807f},
  { -104.545436560947f,    -37.9527138972067f},
  { -105.825786463196f,    -31.7657157810479f},
  { -99.5494059911635f,    -33.9341349165501f}};
 
/* 3LD geosphere 'ico' [12 0] (1442 points) */
const float __geosphere_ico_12_0_dirs_deg[1442][2] =
{ { 31.7174744114610f,    0.0f},
  { 148.282525588539f,    0.0f},
  { -148.282525588539f,    0.0f},
  { -31.7174744114610f,    0.0f},
  { 0.0f,    58.2825255885390f},
  { 0.0f,    -58.2825255885390f},
  { 180.0f,    -58.2825255885390f},
  { 180.0f,    58.2825255885390f},
  { 90.0f,    31.7174744114610f},
  { -90.0f,    31.7174744114610f},
  { -90.0f,    -31.7174744114610f},
  { 90.0f,    -31.7174744114610f},
  { 0.0f,    62.7502499362301f},
  { 0.0f,    67.6072290710451f},
  { 0.0f,    72.8279621494862f},
  { 0.0f,    78.3592768632294f},
  { 0.0f,    84.1189512527134f},
  { 0.0f,    90.0f},
  { 180.0f,    84.1189512527134f},
  { 180.0f,    78.3592768632294f},
  { 180.0f,    72.8279621494862f},
  { 180.0f,    67.6072290710451f},
  { 180.0f,    62.7502499362301f},
  { 8.36785885565049f,    59.3976574802411f},
  { 10.1918500362761f,    64.0598368480186f},
  { 13.0152040462228f,    69.0835941901292f},
  { 17.9319334355159f,    74.3810971336279f},
  { 28.3399673707642f,    79.7227786716467f},
  { 58.2825255885390f,    84.2221928049541f},
  { 121.717474411461f,    84.2221928049541f},
  { 151.660032629236f,    79.7227786716467f},
  { 162.068066564484f,    74.3810971336279f},
  { 166.984795953777f,    69.0835941901292f},
  { 169.808149963724f,    64.0598368480186f},
  { 171.632141144350f,    59.3976574802411f},
  { 17.9319334355159f,    59.9665693791348f},
  { 22.0237505161462f,    64.6075511946472f},
  { 28.3399673707642f,    69.4455573432933f},
  { 38.9734473368657f,    74.1982775048736f},
  { 58.2825255885390f,    78.1814142633759f},
  { 90.0f,    79.9071595156824f},
  { 121.717474411461f,    78.1814142633759f},
  { 141.026552663134f,    74.1982775048736f},
  { 151.660032629236f,    69.4455573432933f},
  { 157.976249483854f,    64.6075511946472f},
  { 162.068066564484f,    59.9665693791348f},
  { 28.3399673707642f,    59.7900946927798f},
  { 34.7391081893039f,    64.1249435633682f},
  { 44.1517511327961f,    68.3569826266350f},
  { 58.2825255885390f,    72.0f},
  { 78.3592768632294f,    74.2410708523759f},
  { 101.640723136771f,    74.2410708523759f},
  { 121.717474411461f,    72.0f},
  { 135.848248867204f,    68.3569826266350f},
  { 145.260891810696f,    64.1249435633682f},
  { 151.660032629236f,    59.7900946927798f},
  { 38.9734473368657f,    58.7297899739513f},
  { 47.1679114977869f,    62.4871807253393f},
  { 58.2825255885390f,    65.8185857366241f},
  { 72.8279621494862f,    68.2090865913442f},
  { 90.0f,    69.0948425521107f},
  { 107.172037850514f,    68.2090865913442f},
  { 121.717474411461f,    65.8185857366241f},
  { 132.832088502213f,    62.4871807253393f},
  { 141.026552663134f,    58.7297899739513f},
  { 49.1320813134511f,    56.7641893271062f},
  { 58.2825255885390f,    59.7778071950459f},
  { 69.6541923856616f,    62.1433456787522f},
  { 82.9535936191428f,    63.4669072935504f},
  { 97.0464063808572f,    63.4669072935504f},
  { 110.345807614338f,    62.1433456787522f},
  { 121.717474411461f,    59.7778071950459f},
  { 130.867918686549f,    56.7641893271062f},
  { 58.2825255885390f,    54.0f},
  { 67.6072290710451f,    56.2397210741351f},
  { 78.3592768632294f,    57.7475579750497f},
  { 90.0f,    58.2825255885390f},
  { 101.640723136771f,    57.7475579750497f},
  { 112.392770928955f,    56.2397210741351f},
  { 121.717474411461f,    54.0f},
  { 66.1808024884231f,    50.6327247195825f},
  { 75.1646413480039f,    52.1723325493831f},
  { 84.9544063480986f,    53.0023277621793f},
  { 95.0455936519014f,    53.0023277621793f},
  { 104.835358651996f,    52.1723325493831f},
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  { -137.329533687801f,    -13.6853671173645f},
  { -139.073571574690f,    -53.3421784101822f},
  { -137.470208624967f,    -47.5637193063793f},
  { -136.132253030241f,    -41.4939010991043f},
  { -135.0f,    -35.2643896827547f},
  { -134.030110218405f,    -29.0258428248200f},
  { -133.190450300436f,    -22.9282785675942f},
  { -132.456739125343f,    -17.1013346715150f},
  { -129.964753678737f,    -51.1183373464232f},
  { -129.222929357691f,    -45.1435105228856f},
  { -128.602952180105f,    -38.9522209765831f},
  { -128.077195298403f,    -32.6839097448066f},
  { -127.625768562624f,    -26.4879839228922f},
  { -127.233995684556f,    -20.5035260967303f},
  { -121.717474411461f,    -48.2221928049541f},
  { -121.717474411461f,    -42.1814142633759f},
  { -121.717474411461f,    -36.0f},
  { -121.717474411461f,    -29.8185857366241f},
  { -121.717474411461f,    -23.7778071950459f},
  { -114.502477634306f,    -44.8430231404270f},
  { -115.077437696012f,    -38.8577003880126f},
  { -115.567851058280f,    -32.8030205324522f},
  { -115.991030692267f,    -26.8136666500115f},
  { -108.323726945222f,    -41.1884885194893f},
  { -109.309078251673f,    -35.3584095083404f},
  { -110.161225333132f,    -29.5214139777455f},
  { -103.088026760372f,    -37.4462884164009f},
  { -104.346731310829f,    -31.8445438275894f},
  { -98.6643878136606f,    -33.7636228467164f}};
 
/* 3LD geosphere 'ico' [13 0] (1692 points) */
const float __geosphere_ico_13_0_dirs_deg[1692][2] =
{ { 31.7174744114610f,    0.0f},
  { 148.282525588539f,    0.0f},
  { -148.282525588539f,    0.0f},
  { -31.7174744114610f,    0.0f},
  { 0.0f,    58.2825255885390f},
  { 0.0f,    -58.2825255885390f},
  { 180.0f,    -58.2825255885390f},
  { 180.0f,    58.2825255885390f},
  { 90.0f,    31.7174744114610f},
  { -90.0f,    31.7174744114610f},
  { -90.0f,    -31.7174744114610f},
  { 90.0f,    -31.7174744114610f},
  { 0.0f,    62.3925997209885f},
  { 0.0f,    66.8353860746534f},
  { 0.0f,    71.5932006647639f},
  { 0.0f,    76.6286429612929f},
  { 0.0f,    81.8830323534313f},
  { 0.0f,    87.2781463566519f},
  { 180.0f,    87.2781463566519f},
  { 180.0f,    81.8830323534313f},
  { 180.0f,    76.6286429612929f},
  { 180.0f,    71.5932006647639f},
  { 180.0f,    66.8353860746534f},
  { 180.0f,    62.3925997209885f},
  { 7.67922857366964f,    59.3286053642054f},
  { 9.19099647608508f,    63.6106663265394f},
  { 11.4340697442537f,    68.2096620005233f},
  { 15.0920752881032f,    73.0708132363913f},
  { 22.0237505161462f,    78.0665504624893f},
  { 38.9734473368657f,    82.8183370989074f},
  { 90.0f,    85.4686859541220f},
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  { 19.7767131841238f,    64.2159562975888f},
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  { 38.9734473368657f,    68.0814487319598f},
  { 50.5099309427673f,    71.8439998608869f},
  { 67.6072290710451f,    74.6921232020624f},
  { 90.0000000000000f,    75.7979510216779f},
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  { 129.490069057233f,    71.8439998608869f},
  { 141.026552663134f,    68.0814487319598f},
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  { 42.7561895905164f,    62.8150947166279f},
  { 52.3123893000598f,    66.2217370325843f},
  { 65.1310748815380f,    68.9778919653611f},
  { 81.2167693990410f,    70.5667382332046f},
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  { 144.279098000866f,    59.1541202718966f},
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  { 63.6909565444517f,    63.3000410294001f},
  { 76.1141128518623f,    65.0887998071003f},
  { 90.0f,    65.7317808244396f},
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  { 134.678915564518f,    57.6230740536504f},
  { 54.2069014710865f,    55.3639291306766f},
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  { 95.8810487472866f,    60.6081893164628f},
  { 107.172037850514f,    59.6100403971132f},
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  { 70.5487009486867f,    54.2869960799927f},
  { 79.9858774849308f,    55.4575554335454f},
  { 90.0f,    55.8672503778391f},
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  { 109.451299051313f,    54.2869960799927f},
  { 117.912111400503f,    52.5072028198446f},
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  { -139.299999410873f,    17.5553136605234f},
  { -133.935794277710f,    15.6181902414563f},
  { -148.843167443314f,    15.9208749961433f},
  { -143.543377358329f,    14.2666249148246f},
  { -138.323420251550f,    12.4971076405263f},
  { -147.419639185256f,    11.1079714409386f},
  { -142.388644576228f,    9.47109376781113f},
  { -146.129299783167f,    6.59609223407253f},
  { -168.278384807134f,    -55.5683540408088f},
  { -164.711859062464f,    -51.3862242437938f},
  { -161.565051177078f,    -46.8204952158267f},
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  { -156.319382182471f,    -36.7986876565218f},
  { -154.127928592099f,    -31.5236664757459f},
  { -152.172037850514f,    -26.2153012260126f},
  { -150.419565989699f,    -20.9821608982710f},
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  { -151.759148035263f,    -41.0697333442294f},
  { -149.692611957303f,    -35.6550166885512f},
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  { -141.627957235047f,    -28.4456554391894f},
  { -140.394284756739f,    -22.8984738947884f},
  { -139.299999410873f,    -17.5553136605234f},
  { -138.323420251550f,    -12.4971076405263f},
  { -142.156791984719f,    -54.2915904436854f},
  { -140.386297782898f,    -49.0757348734261f},
  { -138.889512261975f,    -43.5782038962524f},
  { -137.609162359726f,    -37.8954593557137f},
  { -136.502510907796f,    -32.1421016882594f},
  { -135.537137409656f,    -26.4390750029195f},
  { -134.688068424517f,    -20.8997946068491f},
  { -133.935794277710f,    -15.6181902414563f},
  { -133.472742324446f,    -52.5033623066590f},
  { -132.469522203645f,    -47.0762912260020f},
  { -131.622492959303f,    -41.4235128973441f},
  { -130.898110732937f,    -35.6494412835039f},
  { -130.271724440412f,    -29.8716190222766f},
  { -129.724831969882f,    -24.2073506421853f},
  { -129.243286808989f,    -18.7602981099717f},
  { -125.428820348224f,    -50.0840260637785f},
  { -125.124247141936f,    -44.5468124755062f},
  { -124.865825976588f,    -38.8428070417901f},
  { -124.643814022546f,    -33.0807088681832f},
  { -124.451028529565f,    -27.3758768211569f},
  { -124.282058316783f,    -21.8369553839562f},
  { -118.231628410980f,    -47.1655463617031f},
  { -118.501697258017f,    -41.6186650159532f},
  { -118.732962674865f,    -35.9630277751952f},
  { -118.933220885046f,    -30.3070063208102f},
  { -119.108312051735f,    -24.7589480673360f},
  { -111.944105498296f,    -43.9101112683018f},
  { -112.650200416646f,    -38.4424112745958f},
  { -113.261836321706f,    -32.9199372930422f},
  { -113.796664113265f,    -27.4459913473483f},
  { -106.527984084055f,    -40.4791269870344f},
  { -107.544019585615f,    -35.1618531958101f},
  { -108.434948822922f,    -29.8371409870851f},
  { -101.892235676848f,    -37.0120512651164f},
  { -103.116054327274f,    -31.8970076530459f},
  { -97.9285379327587f,    -33.6165047722674f}};
 
/* 3LD geosphere 'ico' [14 0] (1962 points) */
const float __geosphere_ico_14_0_dirs_deg[1962][2] =
{ { 31.7174744114610f,    0.0f},
  { 148.282525588539f,    0.0f},
  { -148.282525588539f,    0.0f},
  { -31.7174744114610f,    0.0f},
  { 0.0f,    58.2825255885390f},
  { 0.0f,    -58.2825255885390f},
  { 180.0f,    -58.2825255885390f},
  { 180.0f,    58.2825255885390f},
  { 90.0f,    31.7174744114610f},
  { -90.0f,    31.7174744114610f},
  { -90.0f,    -31.7174744114610f},
  { 90.0f,    -31.7174744114610f},
  { 0.0f,    62.0878885994974f},
  { 0.0f,    66.1808024884231f},
  { 0.0f,    70.5487009486867f},
  { 0.0f,    75.1646413480039f},
  { 0.0f,    79.9858774849308f},
  { 0.0f,    84.9544063480986f},
  { 0.0f,    90.0f},
  { 180.0f,    84.9544063480986f},
  { 180.0f,    79.9858774849308f},
  { 180.0f,    75.1646413480039f},
  { 180.0f,    70.5487009486867f},
  { 180.0f,    66.1808024884231f},
  { 180.0f,    62.0878885994974f},
  { 7.09478492022928f,    59.2669202265768f},
  { 8.36785885565049f,    63.2249334105983f},
  { 10.1918500362761f,    67.4615581142125f},
  { 13.0152040462228f,    71.9408793552494f},
  { 17.9319334355159f,    76.5853803432626f},
  { 28.3399673707642f,    81.2065723886572f},
  { 58.2825255885390f,    85.0661994333044f},
  { 121.717474411461f,    85.0661994333044f},
  { 151.660032629236f,    81.2065723886572f},
  { 162.068066564484f,    76.5853803432626f},
  { 166.984795953777f,    71.9408793552494f},
  { 169.808149963724f,    67.4615581142125f},
  { 171.632141144350f,    63.2249334105983f},
  { 172.905215079771f,    59.2669202265768f},
  { 15.0920752881032f,    59.8719245592249f},
  { 17.9319334355159f,    63.8594901030400f},
  { 22.0237505161462f,    68.0530702426802f},
  { 28.3399673707642f,    72.3432296064903f},
  { 38.9734473368657f,    76.4911891305542f},
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  { 157.976249483854f,    68.0530702426802f},
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  { 164.907924711897f,    59.8719245592249f},
  { 23.8110044533781f,    59.9680684957604f},
  { 28.3399673707642f,    63.8188491077792f},
  { 34.7391081893039f,    67.7275573789671f},
  { 44.1517511327961f,    71.4761517051299f},
  { 58.2825255885390f,    74.6575963529091f},
  { 78.3592768632294f,    76.5969610856024f},
  { 101.640723136771f,    76.5969610856024f},
  { 121.717474411461f,    74.6575963529091f},
  { 135.848248867204f,    71.4761517051299f},
  { 145.260891810696f,    67.7275573789671f},
  { 151.660032629236f,    63.8188491077792f},
  { 156.188995546622f,    59.9680684957604f},
  { 32.9114931857064f,    59.4482400957790f},
  { 38.9734473368657f,    62.9823782611085f},
  { 47.1679114977869f,    66.3788444575833f},
  { 58.2825255885390f,    69.3424036470909f},
  { 72.8279621494862f,    71.4441996352265f},
  { 90.0f,    72.2181794238810f},
  { 107.172037850514f,    71.4441996352265f},
  { 121.717474411461f,    69.3424036470909f},
  { 132.832088502213f,    66.3788444575833f},
  { 141.026552663134f,    62.9823782611085f},
  { 147.088506814294f,    59.4482400957790f},
  { 41.9526190816497f,    58.2581213197305f},
  { 49.1320813134511f,    61.3267760588334f},
  { 58.2825255885390f,    64.0724667392235f},
  { 69.6541923856616f,    66.1988092480856f},
  { 82.9535936191428f,    67.3781928139341f},
  { 97.0464063808572f,    67.3781928139341f},
  { 110.345807614338f,    66.1988092480856f},
  { 121.717474411461f,    64.0724667392235f},
  { 130.867918686549f,    61.3267760588334f},
  { 138.047380918350f,    58.2581213197305f},
  { 50.5099309427673f,    56.4143320128269f},
  { 58.2825255885390f,    58.9338005666956f},
  { 67.6072290710451f,    61.0023561147386f},
  { 78.3592768632294f,    62.3804108615600f},
  { 90.0f,    62.8666219591469f},
  { 101.640723136771f,    62.3804108615600f},
  { 112.392770928955f,    61.0023561147386f},
  { 121.717474411461f,    58.9338005666956f},
  { 129.490069057233f,    56.4143320128269f},
  { 58.2825255885390f,    54.0f},
  { 66.1808024884231f,    55.9579589628024f},
  { 75.1646413480039f,    57.4073382612483f},
  { 84.9544063480986f,    58.1829563353826f},
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  { 104.835358651996f,    57.4073382612483f},
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  { 121.717474411461f,    54.0f},
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  { 72.8279621494862f,    52.5810709845051f},
  { 81.2167693990410f,    53.5115270803982f},
  { 90.0f,    53.8340928444730f},
  { 98.7832306009590f,    53.5115270803982f},
  { 107.172037850514f,    52.5810709845051f},
  { 114.868925118462f,    51.1421142488325f},
  { 71.0499775117081f,    47.9838604695474f},
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  { 76.1141128518623f,    44.6623463365959f},
  { 82.9535936191428f,    45.2948319044883f},
  { 90.0f,    45.5120052212781f},
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  { 80.4324561201698f,    41.2951365783062f},
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  { 93.2157771534443f,    41.6485706123396f},
  { 99.5675438798302f,    41.2951365783062f},
  { 84.1189512527134f,    37.9745512724670f},
  { 90.0f,    38.1213002554066f},
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  { 87.2781463566518f,    34.7673390037789f},
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  { -32.9114931857064f,    59.4482400957790f},
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  { -90.0f,    38.1213002554066f},
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  { -90.0f,    62.8666219591469f},
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  { -116.224723062259f,    -35.8746974937919f},
  { -116.565051177078f,    -30.6726725373555f},
  { -116.865761745829f,    -25.5544940369357f},
  { -109.849717733457f,    -43.0802347503797f},
  { -110.632446085536f,    -38.0549736525038f},
  { -111.319382182471f,    -32.9853991131827f},
  { -111.926931054324f,    -27.9522875976322f},
  { -105.045343845740f,    -39.8605646102295f},
  { -106.066779114954f,    -34.9768443320308f},
  { -106.972905786530f,    -30.0855362676247f},
  { -100.894233011422f,    -36.6365158565735f},
  { -102.076935012264f,    -31.9320345172748f},
  { -97.3072664728573f,    -33.4884987864554f}};
 
/* 3LD geosphere 'ico' [15 0] (2252 points) */
const float __geosphere_ico_15_0_dirs_deg[2252][2] =
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  { 148.282525588539f,    0.0f},
  { -148.282525588539f,    0.0f},
  { -31.7174744114610f,    0.0f},
  { 0.0f,    58.2825255885390f},
  { 0.0f,    -58.2825255885390f},
  { 180.0f,    -58.2825255885390f},
  { 180.0f,    58.2825255885390f},
  { 90.0f,    31.7174744114610f},
  { -90.0f,    31.7174744114610f},
  { -90.0f,    -31.7174744114610f},
  { 90.0f,    -31.7174744114610f},
  { 0.0f,    61.8251865351426f},
  { 0.0f,    65.6187815578030f},
  { 0.0f,    69.6541923856616f},
  { 0.0f,    73.9115997418271f},
  { 0.0f,    78.3592768632294f},
  { 0.0f,    82.9535936191428f},
  { 0.0f,    87.6406185690461f},
  { 180.0f,    87.6406185690461f},
  { 180.0f,    82.9535936191428f},
  { 180.0f,    78.3592768632294f},
  { 180.0f,    73.9115997418271f},
  { 180.0f,    69.6541923856616f},
  { 180.0f,    65.6187815578030f},
  { 180.0f,    61.8251865351426f},
  { 6.59264467355895f,    59.2116443441111f},
  { 7.67922857366964f,    62.8903831093188f},
  { 9.19099647608508f,    66.8151622059356f},
  { 11.4340697442537f,    70.9614896019555f},
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  { 22.0237505161462f,    79.6613630728832f},
  { 38.9734473368657f,    83.7926432688605f},
  { 90.0f,    86.0865699753911f},
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  { 170.809003523915f,    66.8151622059356f},
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  { 155.189115239873f,    71.4897072290348f},
  { 160.223286815876f,    67.4513372081180f},
  { 163.606749851527f,    63.5367057973473f},
  { 166.021562661129f,    59.8179223197217f},
  { 22.0237505161462f,    59.9952713133382f},
  { 25.8924090881804f,    63.6240862949495f},
  { 31.2478160930689f,    67.3424609596128f},
  { 38.9734473368657f,    71.0021166134344f},
  { 50.5099309427673f,    74.3263225812526f},
  { 67.6072290710451f,    76.8187518549304f},
  { 90.0f,    77.7816801337513f},
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  { 129.490069057233f,    74.3263225812526f},
  { 141.026552663134f,    71.0021166134344f},
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  { 30.4715337744227f,    59.6513563396351f},
  { 35.7209019991337f,    63.0444971189200f},
  { 42.7561895905164f,    66.3777711696528f},
  { 52.3123893000598f,    69.4343887930543f},
  { 65.1310748815380f,    71.8790718535498f},
  { 81.2167693990410f,    73.2780371655037f},
  { 98.7832306009590f,    73.2780371655037f},
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  { 144.279098000866f,    63.0444971189200f},
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  { 38.9734473368657f,    58.7297899739513f},
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  { 63.6909565444517f,    66.9209866913203f},
  { 76.1141128518623f,    68.5221100088469f},
  { 90.0f,    69.0948425521107f},
  { 103.885887148138f,    68.5221100088469f},
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  { 126.562139238749f,    64.5666406655263f},
  { 134.678915564518f,    61.7562141472517f},
  { 141.026552663134f,    58.7297899739513f},
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  { 90.0f,    52.1031151288303f},
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  { -118.859981875649f,    -43.3183341586149f},
  { -119.044094519285f,    -38.4329531156089f},
  { -119.205932247399f,    -33.5113110478349f},
  { -119.349304703493f,    -28.6254919805188f},
  { -119.477200063791f,    -23.8444836331026f},
  { -113.038132901993f,    -45.3018275871428f},
  { -113.600506764892f,    -40.5649232343349f},
  { -114.094842552111f,    -35.7584993532105f},
  { -114.532721253561f,    -30.9502839364211f},
  { -114.923248725310f,    -26.2079258130924f},
  { -108.107934083465f,    -42.3426786955557f},
  { -108.932564333371f,    -37.6983190307739f},
  { -109.664369085192f,    -33.0173980941400f},
  { -110.317983451487f,    -28.3641579940766f},
  { -103.802042319059f,    -39.3183133212560f},
  { -104.813827615902f,    -34.8051847162798f},
  { -105.720276558449f,    -30.2845539162313f},
  { -100.049175517616f,    -36.3090746817282f},
  { -101.188427726582f,    -31.9552588002486f},
  { -96.7758625813643f,    -33.3762411909610f}};
 
/* 3LD geosphere 'ico' [16 0] (2562 points) */
const float __geosphere_ico_16_0_dirs_deg[2562][2] =
{ { 31.7174744114610f,    0.0f},
  { 148.282525588539f,    0.0f},
  { -148.282525588539f,    0.0f},
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  { 0.0f,    58.2825255885390f},
  { 0.0f,    -58.2825255885390f},
  { 180.0f,    -58.2825255885390f},
  { 180.0f,    58.2825255885390f},
  { 90.0f,    31.7174744114610f},
  { -90.0f,    31.7174744114610f},
  { -90.0f,    -31.7174744114610f},
  { 90.0f,    -31.7174744114610f},
  { 0.0f,    61.5963754664474f},
  { 0.0f,    65.1310748815380f},
  { 0.0f,    68.8798871556760f},
  { 0.0f,    72.8279621494862f},
  { 0.0f,    76.9513489599765f},
  { 0.0f,    81.2167693990410f},
  { 0.0f,    85.5824320004692f},
  { 0.0f,    90.0f},
  { 180.0f,    85.5824320004692f},
  { 180.0f,    81.2167693990410f},
  { 180.0f,    76.9513489599765f},
  { 180.0f,    72.8279621494862f},
  { 180.0f,    68.8798871556760f},
  { 180.0f,    65.1310748815380f},
  { 180.0f,    61.5963754664474f},
  { 6.15662931139232f,    59.1619275753025f},
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  { 8.36785885565049f,    66.2517584756324f},
  { 10.1918500362761f,    70.1070308125077f},
  { 13.0152040462228f,    74.1292066099994f},
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  { 166.984795953777f,    59.7634611728920f},
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  { 156.188995546622f,    63.4231532306817f},
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  { 38.9734473368657f,    66.2771675744593f},
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  { 90.0f,    74.5495629136742f},
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  { 36.3333661325874f,    59.0812124975607f},
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  { 121.717474411461f,    -31.3560642989362f},
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  { 113.228022928220f,    -26.7511554968076f},
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  { 141.550822966496f,    -34.3505184589462f},
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  { 121.717474411461f,    -22.3045403104627f},
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  { 149.327327462644f,    -27.9936984541352f},
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  { 129.755171678152f,    -17.3827856796100f},
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  { 133.522338790263f,    -14.8566700706480f},
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  { 145.609145696363f,    -15.2134343179303f},
  { 141.313021975992f,    -13.8129800206087f},
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  { 148.721195693252f,    -12.5818702829736f},
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  { 143.615372719585f,    -7.53020899059060f},
  { 146.562704124137f,    -5.27729717955544f},
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  { -163.839273313454f,    56.5462580056053f},
  { -156.738163678295f,    56.5250600061002f},
  { -149.366869438509f,    56.0699480487420f},
  { -141.959700313972f,    55.1436992467066f},
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  { -167.437504668780f,    52.9500102616329f},
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  { -154.291030110658f,    52.7767392956372f},
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  { -121.717474411461f,    45.2276448816065f},
  { -116.440141502986f,    42.7360072735219f},
  { -111.703351896392f,    40.0910997872291f},
  { -107.483322113027f,    37.3720700573987f},
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  { -100.420348572588f,    31.9703418211533f},
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  { -121.717474411461f,    40.6439357010638f},
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  { -112.268467211959f,    35.6285964660136f},
  { -108.239630439654f,    33.0274403302419f},
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  { -121.717474411461f,    36.0f},
  { -117.034709495470f,    33.6160922031027f},
  { -112.773700332310f,    31.1637336664207f},
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  { -154.269725630114f,    41.1217160940118f},
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  { -121.717474411461f,    -45.2276448816065f},
  { -121.717474411461f,    -40.6439357010638f},
  { -121.717474411461f,    -36.0f},
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  { -121.717474411461f,    -26.7723551183935f},
  { -121.717474411461f,    -22.3045403104628f},
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  { -116.440141502986f,    -42.7360072735219f},
  { -116.755127470617f,    -38.1909250447259f},
  { -117.034709495470f,    -33.6160922031027f},
  { -117.284527656332f,    -29.0697052196415f},
  { -117.509086510999f,    -24.6077737779805f},
  { -111.067169971118f,    -44.4965112658956f},
  { -111.703351896392f,    -40.0910997872291f},
  { -112.268467211959f,    -35.6285964660136f},
  { -112.773700332310f,    -31.1637336664207f},
  { -113.228022928220f,    -26.7511554968076f},
  { -106.639167039584f,    -41.6860404488482f},
  { -107.483322113027f,    -37.3720700573987f},
  { -108.239630439654f,    -33.0274403302419f},
  { -108.920899457445f,    -28.7040129778536f},
  { -102.745388178883f,    -38.8402116496635f},
  { -103.738656574656f,    -34.6470309014331f},
  { -104.636053416868f,    -30.4465738857480f},
  { -99.3247034825061f,    -36.0213780600392f},
  { -100.420348572588f,    -31.9703418211533f},
  { -96.3162168546181f,    -33.2770772600221f}};
 
/* 3LD geosphere 'oct' [0 0] (6 points) */
const float __geosphere_oct_0_0_dirs_deg[6][2] =
{ { 0.0f,    0.0f},
  { 180.0f,    0.0f},
  { 90.0f,    0.0f},
  { -90.0f,    0.0f},
  { 0.0f,    90.0f},
  { 0.0f,    -90.0f}};
  
/* 3LD geosphere 'oct' [1 0] (14 points) */
const float __geosphere_oct_1_0_dirs_deg[14][2] =
{ { 0.0f,    0.0f},
  { 180.0f,    0.0f},
  { 90.0f,    0.0f},
  { -90.0f,    0.0f},
  { 0.0f,    90.0f},
  { 0.0f,    -90.0f},
  { 45.0000000000000f,    35.2643896827547f},
  { 135.0f,    35.2643896827547f},
  { -135.0f,    35.2643896827547f},
  { -45.0000000000000f,    35.2643896827547f},
  { 45.0000000000000f,    -35.2643896827547f},
  { 135.0f,    -35.2643896827547f},
  { -135.0f,    -35.2643896827547f},
  { -45.0000000000000f,    -35.2643896827547f}};
 
/* 3LD geosphere 'oct' [2 0] (18 points) */
const float __geosphere_oct_2_0_dirs_deg[18][2] =
{ { 0.0f,    0.0f},
  { 180.0f,    0.0f},
  { 90.0f,    0.0f},
  { -90.0f,    0.0f},
  { 0.0f,    90.0f},
  { 0.0f,    -90.0f},
  { 0.0f,    45.0f},
  { 45.0f,    0.0f},
  { 90.0f,    45.0f},
  { 135.0f,    0.0f},
  { 180.0f,    45.0f},
  { -135.0f,    0.0f},
  { -90.0f,    45.0f},
  { -45.0f,    0.0f},
  { 0.0f,    -45.0f},
  { 90.0f,    -45.0f},
  { 180.0f,    -45.0f},
  { -90.0f,    -45.0f}};
 
/* 3LD geosphere 'oct' [3 0] (38 points) */
const float __geosphere_oct_3_0_dirs_deg[38][2] =
{ { 0.0f,    0.0f},
  { 180.0f,    0.0f},
  { 90.0f,    0.0f},
  { -90.0f,    0.0f},
  { 0.0f,    90.0f},
  { 0.0f,    -90.0f},
  { 0.0f,    26.5650511770780f},
  { 0.0f,    63.4349488229220f},
  { 26.5650511770780f,    0.0f},
  { 45.0000000000000f,    35.2643896827547f},
  { 90.0f,    63.4349488229220f},
  { 63.4349488229220f,    0.0f},
  { 90.0f,    26.5650511770780f},
  { 116.565051177078f,    0.0f},
  { 135.0f,    35.2643896827547f},
  { 180.0f,    63.4349488229220f},
  { 153.434948822922f,    0.0f},
  { 180.0f,    26.5650511770780f},
  { -153.434948822922f,    0.0f},
  { -135.0f,    35.2643896827547f},
  { -90.0f,    63.4349488229220f},
  { -116.565051177078f,    0.0f},
  { -90.0f,    26.5650511770780f},
  { -63.4349488229220f,    0.0f},
  { -45.0000000000000f,    35.2643896827547f},
  { -26.5650511770780f,    0.0f},
  { 0.0f,    -26.5650511770780f},
  { 45.0000000000000f,    -35.2643896827547f},
  { 90.0f,    -26.5650511770780f},
  { 0.0f,    -63.4349488229220f},
  { 90.0f,    -63.4349488229220f},
  { 135.0f,    -35.2643896827547f},
  { 180.0f,    -26.5650511770780f},
  { 180.0f,    -63.4349488229220f},
  { -135.0f,    -35.2643896827547f},
  { -90.0f,    -26.5650511770780f},
  { -90.0f,    -63.4349488229220f},
  { -45.0000000000000f,    -35.2643896827547f}};
 
/* 3LD geosphere 'oct' [4 0] (66 points) */
const float __geosphere_oct_4_0_dirs_deg[66][2] =
{ { 0.0f,    0.0f},
  { 180.0f,    0.0f},
  { 90.0f,    0.0f},
  { -90.0f,    0.0f},
  { 0.0f,    90.0f},
  { 0.0f,    -90.0f},
  { 0.0f,    18.4349488229220f},
  { 0.0f,    45.0f},
  { 0.0f,    71.5650511770780f},
  { 18.4349488229220f,    0.0f},
  { 26.5650511770780f,    24.0948425521107f},
  { 45.0f,    54.7356103172453f},
  { 90.0f,    71.5650511770780f},
  { 45.0f,    0.0f},
  { 63.4349488229220f,    24.0948425521107f},
  { 90.0f,    45.0f},
  { 71.5650511770780f,    0.0f},
  { 90.0f,    18.4349488229220f},
  { 108.434948822922f,    0.0f},
  { 116.565051177078f,    24.0948425521107f},
  { 135.0f,    54.7356103172453f},
  { 180.0f,    71.5650511770780f},
  { 135.0f,    0.0f},
  { 153.434948822922f,    24.0948425521107f},
  { 180.0f,    45.0f},
  { 161.565051177078f,    0.0f},
  { 180.0f,    18.4349488229220f},
  { -161.565051177078f,    0.0f},
  { -153.434948822922f,    24.0948425521107f},
  { -135.0f,    54.7356103172453f},
  { -90.0f,    71.5650511770780f},
  { -135.0f,    0.0f},
  { -116.565051177078f,    24.0948425521107f},
  { -90.0f,    45.0f},
  { -108.434948822922f,    0.0f},
  { -90.0f,    18.4349488229220f},
  { -71.5650511770780f,    0.0f},
  { -63.4349488229220f,    24.0948425521107f},
  { -45.0f,    54.7356103172453f},
  { -45.0f,    0.0f},
  { -26.5650511770780f,    24.0948425521107f},
  { -18.4349488229220f,    0.0f},
  { 0.0f,    -18.4349488229220f},
  { 26.5650511770780f,    -24.0948425521107f},
  { 63.4349488229220f,    -24.0948425521107f},
  { 90.0f,    -18.4349488229220f},
  { 0.0f,    -45.0f},
  { 45.0f,    -54.7356103172453f},
  { 90.0f,    -45.0f},
  { 0.0f,    -71.5650511770780f},
  { 90.0f,    -71.5650511770780f},
  { 116.565051177078f,    -24.0948425521107f},
  { 153.434948822922f,    -24.0948425521107f},
  { 180.0f,    -18.4349488229220f},
  { 135.0f,    -54.7356103172453f},
  { 180.0f,    -45.0f},
  { 180.0f,    -71.5650511770780f},
  { -153.434948822922f,    -24.0948425521107f},
  { -116.565051177078f,    -24.0948425521107f},
  { -90.0f,    -18.4349488229220f},
  { -135.0f,    -54.7356103172453f},
  { -90.0f,    -45.0f},
  { -90.0f,    -71.5650511770780f},
  { -63.4349488229220f,    -24.0948425521107f},
  { -26.5650511770780f,    -24.0948425521107f},
  { -45.0f,    -54.7356103172453f}};
 
/* 3LD geosphere 'oct' [5 0] (102 points) */
const float __geosphere_oct_5_0_dirs_deg[102][2] =
{ { 0.0f,    0.0f},
  { 180.0f,    0.0f},
  { 90.0f,    0.0f},
  { -90.0f,    0.0f},
  { 0.0f,    90.0f},
  { 0.0f,    -90.0f},
  { 0.0f,    14.0362434679265f},
  { 0.0f,    33.6900675259798f},
  { 0.0f,    56.3099324740202f},
  { 0.0f,    75.9637565320735f},
  { 14.0362434679265f,    0.0f},
  { 18.4349488229220f,    17.5484006137923f},
  { 26.5650511770780f,    41.8103148957786f},
  { 45.0f,    64.7605981793211f},
  { 90.0f,    75.9637565320735f},
  { 33.6900675259798f,    0.0f},
  { 45.0f,    19.4712206344907f},
  { 63.4349488229220f,    41.8103148957786f},
  { 90.0f,    56.3099324740202f},
  { 56.3099324740202f,    0.0f},
  { 71.5650511770780f,    17.5484006137923f},
  { 90.0f,    33.6900675259798f},
  { 75.9637565320735f,    0.0f},
  { 90.0f,    14.0362434679265f},
  { 104.036243467927f,    0.0f},
  { 108.434948822922f,    17.5484006137923f},
  { 116.565051177078f,    41.8103148957786f},
  { 135.0f,    64.7605981793211f},
  { 180.0f,    75.9637565320735f},
  { 123.690067525980f,    0.0f},
  { 135.0f,    19.4712206344907f},
  { 153.434948822922f,    41.8103148957786f},
  { 180.0f,    56.3099324740202f},
  { 146.309932474020f,    0.0f},
  { 161.565051177078f,    17.5484006137923f},
  { 180.0f,    33.6900675259798f},
  { 165.963756532074f,    0.0f},
  { 180.0f,    14.0362434679265f},
  { -165.963756532074f,    0.0f},
  { -161.565051177078f,    17.5484006137923f},
  { -153.434948822922f,    41.8103148957786f},
  { -135.0f,    64.7605981793211f},
  { -90.0f,    75.9637565320735f},
  { -146.309932474020f,    0.0f},
  { -135.0f,    19.4712206344907f},
  { -116.565051177078f,    41.8103148957786f},
  { -90.0f,    56.3099324740202f},
  { -123.690067525980f,    0.0f},
  { -108.434948822922f,    17.5484006137923f},
  { -90.0f,    33.6900675259798f},
  { -104.036243467927f,    0.0f},
  { -90.0f,    14.0362434679265f},
  { -75.9637565320735f,    0.0f},
  { -71.5650511770780f,    17.5484006137923f},
  { -63.4349488229220f,    41.8103148957786f},
  { -45.0000000000000f,    64.7605981793211f},
  { -56.3099324740202f,    0.0f},
  { -45.0f,    19.4712206344907f},
  { -26.5650511770780f,    41.8103148957786f},
  { -33.6900675259798f,    0.0f},
  { -18.4349488229220f,    17.5484006137923f},
  { -14.0362434679265f,    0.0f},
  { 0.0f,    -14.0362434679265f},
  { 18.4349488229220f,    -17.5484006137923f},
  { 45.0f,    -19.4712206344907f},
  { 71.5650511770780f,    -17.5484006137923f},
  { 90.0f,    -14.0362434679265f},
  { 0.0f,    -33.6900675259798f},
  { 26.5650511770780f,    -41.8103148957786f},
  { 63.4349488229220f,    -41.8103148957786f},
  { 90.0f,    -33.6900675259798f},
  { 0.0f,    -56.3099324740202f},
  { 45.0f,    -64.7605981793211f},
  { 90.0f,    -56.3099324740202f},
  { 0.0f,    -75.9637565320735f},
  { 90.0f,    -75.9637565320735f},
  { 108.434948822922f,    -17.5484006137923f},
  { 135.0f,    -19.4712206344907f},
  { 161.565051177078f,    -17.5484006137923f},
  { 180.0f,    -14.0362434679265f},
  { 116.565051177078f,    -41.8103148957786f},
  { 153.434948822922f,    -41.8103148957786f},
  { 180.0f,    -33.6900675259798f},
  { 135.0f,    -64.7605981793211f},
  { 180.0f,    -56.3099324740202f},
  { 180.0f,    -75.9637565320735f},
  { -161.565051177078f,    -17.5484006137923f},
  { -135.0f,    -19.4712206344907f},
  { -108.434948822922f,    -17.5484006137923f},
  { -90.0f,    -14.0362434679265f},
  { -153.434948822922f,    -41.8103148957786f},
  { -116.565051177078f,    -41.8103148957786f},
  { -90.0f,    -33.6900675259798f},
  { -135.0f,    -64.7605981793211f},
  { -90.0f,    -56.3099324740202f},
  { -90.0f,    -75.9637565320735f},
  { -71.5650511770780f,    -17.5484006137923f},
  { -45.0f,    -19.4712206344907f},
  { -18.4349488229220f,    -17.5484006137923f},
  { -63.4349488229220f,    -41.8103148957786f},
  { -26.5650511770780f,    -41.8103148957786f},
  { -45.0f,    -64.7605981793211f}};
 
/* 3LD geosphere 'oct' [6 0] (146 points) */
const float __geosphere_oct_6_0_dirs_deg[146][2] =
{ { 0.0f,    0.0f},
  { 180.0f,    0.0f},
  { 90.0f,    0.0f},
  { -90.0f,    0.0f},
  { 0.0f,    90.0f},
  { 0.0f,    -90.0f},
  { 0.0f,    11.3099324740202f},
  { 0.0f,    26.5650511770780f},
  { 0.0f,    45.0f},
  { 0.0f,    63.4349488229220f},
  { 0.0f,    78.6900675259798f},
  { 11.3099324740202f,    0.0f},
  { 14.0362434679265f,    13.6330222253664f},
  { 18.4349488229220f,    32.3115332374239f},
  { 26.5650511770780f,    53.3007747995101f},
  { 45.0000000000000f,    70.5287793655093f},
  { 90.0f,    78.6900675259798f},
  { 26.5650511770780f,    0.0f},
  { 33.6900675259798f,    15.5013595669370f},
  { 45.0000000000000f,    35.2643896827547f},
  { 63.4349488229220f,    53.3007747995101f},
  { 90.0f,    63.4349488229220f},
  { 45.0f,    0.0f},
  { 56.3099324740202f,    15.5013595669370f},
  { 71.5650511770780f,    32.3115332374238f},
  { 90.0f,    45.0f},
  { 63.4349488229220f,    0.0f},
  { 75.9637565320735f,    13.6330222253664f},
  { 90.0f,    26.5650511770780f},
  { 78.6900675259798f,    0.0f},
  { 90.0f,    11.3099324740202f},
  { 101.309932474020f,    0.0f},
  { 104.036243467927f,    13.6330222253664f},
  { 108.434948822922f,    32.3115332374239f},
  { 116.565051177078f,    53.3007747995101f},
  { 135.0f,    70.5287793655093f},
  { 180.0f,    78.6900675259798f},
  { 116.565051177078f,    0.0f},
  { 123.690067525980f,    15.5013595669370f},
  { 135.0f,    35.2643896827547f},
  { 153.434948822922f,    53.3007747995101f},
  { 180.0f,    63.4349488229220f},
  { 135.0f,    0.0f},
  { 146.309932474020f,    15.5013595669370f},
  { 161.565051177078f,    32.3115332374238f},
  { 180.0f,    45.0f},
  { 153.434948822922f,    0.0f},
  { 165.963756532074f,    13.6330222253664f},
  { 180.0f,    26.5650511770780f},
  { 168.690067525980f,    0.0f},
  { 180.0f,    11.3099324740202f},
  { -168.690067525980f,    0.0f},
  { -165.963756532074f,    13.6330222253664f},
  { -161.565051177078f,    32.3115332374239f},
  { -153.434948822922f,    53.3007747995101f},
  { -135.0f,    70.5287793655093f},
  { -90.0f,    78.6900675259798f},
  { -153.434948822922f,    0.0f},
  { -146.309932474020f,    15.5013595669370f},
  { -135.0f,    35.2643896827547f},
  { -116.565051177078f,    53.3007747995101f},
  { -90.0f,    63.4349488229220f},
  { -135.0f,    0.0f},
  { -123.690067525980f,    15.5013595669370f},
  { -108.434948822922f,    32.3115332374238f},
  { -90.0f,    45.0f},
  { -116.565051177078f,    0.0f},
  { -104.036243467927f,    13.6330222253664f},
  { -90.0f,    26.5650511770780f},
  { -101.309932474020f,    0.0f},
  { -90.0f,    11.3099324740202f},
  { -78.6900675259798f,    0.0f},
  { -75.9637565320735f,    13.6330222253664f},
  { -71.5650511770780f,    32.3115332374239f},
  { -63.4349488229220f,    53.3007747995101f},
  { -45.0000000000000f,    70.5287793655093f},
  { -63.4349488229220f,    0.0f},
  { -56.3099324740202f,    15.5013595669370f},
  { -45.0000000000000f,    35.2643896827547f},
  { -26.5650511770780f,    53.3007747995101f},
  { -45.0f,    0.0f},
  { -33.6900675259798f,    15.5013595669370f},
  { -18.4349488229220f,    32.3115332374238f},
  { -26.5650511770780f,    0.0f},
  { -14.0362434679265f,    13.6330222253664f},
  { -11.3099324740202f,    0.0f},
  { 0.0f,    -11.3099324740202f},
  { 14.0362434679265f,    -13.6330222253664f},
  { 33.6900675259798f,    -15.5013595669370f},
  { 56.3099324740202f,    -15.5013595669370f},
  { 75.9637565320735f,    -13.6330222253664f},
  { 90.0f,    -11.3099324740202f},
  { 0.0f,    -26.5650511770780f},
  { 18.4349488229220f,    -32.3115332374238f},
  { 45.0000000000000f,    -35.2643896827547f},
  { 71.5650511770780f,    -32.3115332374238f},
  { 90.0f,    -26.5650511770780f},
  { 0.0f,    -45.0f},
  { 26.5650511770780f,    -53.3007747995101f},
  { 63.4349488229220f,    -53.3007747995101f},
  { 90.0f,    -45.0f},
  { 0.0f,    -63.4349488229220f},
  { 45.0000000000000f,    -70.5287793655093f},
  { 90.0f,    -63.4349488229220f},
  { 0.0f,    -78.6900675259798f},
  { 90.0f,    -78.6900675259798f},
  { 104.036243467927f,    -13.6330222253664f},
  { 123.690067525980f,    -15.5013595669370f},
  { 146.309932474020f,    -15.5013595669370f},
  { 165.963756532074f,    -13.6330222253664f},
  { 180.0f,    -11.3099324740202f},
  { 108.434948822922f,    -32.3115332374238f},
  { 135.0f,    -35.2643896827547f},
  { 161.565051177078f,    -32.3115332374238f},
  { 180.0f,    -26.5650511770780f},
  { 116.565051177078f,    -53.3007747995101f},
  { 153.434948822922f,    -53.3007747995101f},
  { 180.0f,    -45.0f},
  { 135.0f,    -70.5287793655093f},
  { 180.0f,    -63.4349488229220f},
  { 180.0f,    -78.6900675259798f},
  { -165.963756532074f,    -13.6330222253664f},
  { -146.309932474020f,    -15.5013595669370f},
  { -123.690067525980f,    -15.5013595669370f},
  { -104.036243467927f,    -13.6330222253664f},
  { -90.0f,    -11.3099324740202f},
  { -161.565051177078f,    -32.3115332374238f},
  { -135.0f,    -35.2643896827547f},
  { -108.434948822922f,    -32.3115332374238f},
  { -90.0f,    -26.5650511770780f},
  { -153.434948822922f,    -53.3007747995101f},
  { -116.565051177078f,    -53.3007747995101f},
  { -90.0f,    -45.0f},
  { -135.0f,    -70.5287793655093f},
  { -90.0f,    -63.4349488229220f},
  { -90.0f,    -78.6900675259798f},
  { -75.9637565320735f,    -13.6330222253664f},
  { -56.3099324740202f,    -15.5013595669370f},
  { -33.6900675259798f,    -15.5013595669370f},
  { -14.0362434679265f,    -13.6330222253664f},
  { -71.5650511770780f,    -32.3115332374238f},
  { -45.0000000000000f,    -35.2643896827547f},
  { -18.4349488229220f,    -32.3115332374238f},
  { -63.4349488229220f,    -53.3007747995101f},
  { -26.5650511770780f,    -53.3007747995101f},
  { -45.0000000000000f,    -70.5287793655093f}};
 
/* 3LD geosphere 'oct' [7 0] (198 points) */
const float __geosphere_oct_7_0_dirs_deg[198][2] =
{ { 0.0f,    0.0f},
  { 180.0f,    0.0f},
  { 90.0f,    0.0f},
  { -90.0f,    0.0f},
  { 0.0f,    90.0f},
  { 0.0f,    -90.0f},
  { 0.0f,    9.46232220802562f},
  { 0.0f,    21.8014094863518f},
  { 0.0f,    36.8698976458440f},
  { 0.0f,    53.1301023541560f},
  { 0.0f,    68.1985905136482f},
  { 0.0f,    80.5376777919744f},
  { 9.46232220802562f,    0.0f},
  { 11.3099324740202f,    11.0958032831364f},
  { 14.0362434679265f,    25.8766900608275f},
  { 18.4349488229220f,    43.4915193450920f},
  { 26.5650511770780f,    60.7940677526006f},
  { 45.0000000000000f,    74.2068309517361f},
  { 90.0f,    80.5376777919744f},
  { 21.8014094863518f,    0.0f},
  { 26.5650511770780f,    12.6043826483792f},
  { 33.6900675259798f,    29.0171406246015f},
  { 45.0000000000000f,    46.6861433417170f},
  { 63.4349488229220f,    60.7940677526006f},
  { 90.0f,    68.1985905136482f},
  { 36.8698976458440f,    0.0f},
  { 45.0f,    13.2626760083048f},
  { 56.3099324740202f,    29.0171406246015f},
  { 71.5650511770780f,    43.4915193450920f},
  { 90.0f,    53.1301023541560f},
  { 53.1301023541560f,    0.0f},
  { 63.4349488229220f,    12.6043826483792f},
  { 75.9637565320735f,    25.8766900608275f},
  { 90.0f,    36.8698976458440f},
  { 68.1985905136482f,    0.0f},
  { 78.6900675259798f,    11.0958032831364f},
  { 90.0f,    21.8014094863518f},
  { 80.5376777919744f,    0.0f},
  { 90.0f,    9.46232220802562f},
  { 99.4623222080256f,    0.0f},
  { 101.309932474020f,    11.0958032831364f},
  { 104.036243467927f,    25.8766900608275f},
  { 108.434948822922f,    43.4915193450920f},
  { 116.565051177078f,    60.7940677526006f},
  { 135.000000000000f,    74.2068309517361f},
  { 180.0f,    80.5376777919744f},
  { 111.801409486352f,    0.0f},
  { 116.565051177078f,    12.6043826483792f},
  { 123.690067525980f,    29.0171406246015f},
  { 135.0f,    46.6861433417170f},
  { 153.434948822922f,    60.7940677526006f},
  { 180.0f,    68.1985905136482f},
  { 126.869897645844f,    0.0f},
  { 135.0f,    13.2626760083048f},
  { 146.309932474020f,    29.0171406246015f},
  { 161.565051177078f,    43.4915193450920f},
  { 180.0f,    53.1301023541560f},
  { 143.130102354156f,    0.0f},
  { 153.434948822922f,    12.6043826483792f},
  { 165.963756532074f,    25.8766900608275f},
  { 180.0f,    36.8698976458440f},
  { 158.198590513648f,    0.0f},
  { 168.690067525980f,    11.0958032831364f},
  { 180.0f,    21.8014094863518f},
  { 170.537677791974f,    0.0f},
  { 180.0f,    9.46232220802562f},
  { -170.537677791974f,    0.0f},
  { -168.690067525980f,    11.0958032831364f},
  { -165.963756532074f,    25.8766900608275f},
  { -161.565051177078f,    43.4915193450920f},
  { -153.434948822922f,    60.7940677526006f},
  { -135.0f,    74.2068309517361f},
  { -90.0f,    80.5376777919744f},
  { -158.198590513648f,    0.0f},
  { -153.434948822922f,    12.6043826483792f},
  { -146.309932474020f,    29.0171406246015f},
  { -135.0f,    46.6861433417170f},
  { -116.565051177078f,    60.7940677526006f},
  { -90.0f,    68.1985905136482f},
  { -143.130102354156f,    0.0f},
  { -135.0f,    13.2626760083048f},
  { -123.690067525980f,    29.0171406246015f},
  { -108.434948822922f,    43.4915193450920f},
  { -90.0f,    53.1301023541560f},
  { -126.869897645844f,    0.0f},
  { -116.565051177078f,    12.6043826483792f},
  { -104.036243467927f,    25.8766900608275f},
  { -90.0f,    36.8698976458440f},
  { -111.801409486352f,    0.0f},
  { -101.309932474020f,    11.0958032831364f},
  { -90.0f,    21.8014094863518f},
  { -99.4623222080256f,    0.0f},
  { -90.0f,    9.46232220802562f},
  { -80.5376777919744f,    0.0f},
  { -78.6900675259798f,    11.0958032831364f},
  { -75.9637565320735f,    25.8766900608275f},
  { -71.5650511770780f,    43.4915193450920f},
  { -63.4349488229220f,    60.7940677526006f},
  { -45.0000000000000f,    74.2068309517361f},
  { -68.1985905136482f,    0.0f},
  { -63.4349488229220f,    12.6043826483792f},
  { -56.3099324740202f,    29.0171406246015f},
  { -45.0000000000000f,    46.6861433417170f},
  { -26.5650511770780f,    60.7940677526006f},
  { -53.1301023541560f,    0.0f},
  { -45.0f,    13.2626760083048f},
  { -33.6900675259798f,    29.0171406246015f},
  { -18.4349488229220f,    43.4915193450920f},
  { -36.8698976458440f,    0.0f},
  { -26.5650511770780f,    12.6043826483792f},
  { -14.0362434679265f,    25.8766900608275f},
  { -21.8014094863518f,    0.0f},
  { -11.3099324740202f,    11.0958032831364f},
  { -9.46232220802562f,    0.0f},
  { 0.0f,    -9.46232220802562f},
  { 11.3099324740202f,    -11.0958032831364f},
  { 26.5650511770780f,    -12.6043826483792f},
  { 45.0f,    -13.2626760083048f},
  { 63.4349488229220f,    -12.6043826483792f},
  { 78.6900675259798f,    -11.0958032831364f},
  { 90.0f,    -9.46232220802562f},
  { 0.0f,    -21.8014094863518f},
  { 14.0362434679265f,    -25.8766900608275f},
  { 33.6900675259798f,    -29.0171406246015f},
  { 56.3099324740202f,    -29.0171406246015f},
  { 75.9637565320735f,    -25.8766900608275f},
  { 90.0f,    -21.8014094863518f},
  { 0.0f,    -36.8698976458440f},
  { 18.4349488229220f,    -43.4915193450920f},
  { 45.0f,    -46.6861433417170f},
  { 71.5650511770780f,    -43.4915193450920f},
  { 90.0f,    -36.8698976458440f},
  { 0.0f,    -53.1301023541560f},
  { 26.5650511770780f,    -60.7940677526006f},
  { 63.4349488229220f,    -60.7940677526006f},
  { 90.0f,    -53.1301023541560f},
  { 0.0f,    -68.1985905136482f},
  { 45.0f,    -74.2068309517360f},
  { 90.0f,    -68.1985905136482f},
  { 0.0f,    -80.5376777919744f},
  { 90.0f,    -80.5376777919744f},
  { 101.309932474020f,    -11.0958032831364f},
  { 116.565051177078f,    -12.6043826483792f},
  { 135.0f,    -13.2626760083048f},
  { 153.434948822922f,    -12.6043826483792f},
  { 168.690067525980f,    -11.0958032831364f},
  { 180.0f,    -9.46232220802562f},
  { 104.036243467927f,    -25.8766900608275f},
  { 123.690067525980f,    -29.0171406246015f},
  { 146.309932474020f,    -29.0171406246015f},
  { 165.963756532074f,    -25.8766900608275f},
  { 180.0f,    -21.8014094863518f},
  { 108.434948822922f,    -43.4915193450920f},
  { 135.0f,    -46.6861433417170f},
  { 161.565051177078f,    -43.4915193450920f},
  { 180.0f,    -36.8698976458440f},
  { 116.565051177078f,    -60.7940677526006f},
  { 153.434948822922f,    -60.7940677526006f},
  { 180.0f,    -53.1301023541560f},
  { 135.0f,    -74.2068309517360f},
  { 180.0f,    -68.1985905136482f},
  { 180.0f,    -80.5376777919744f},
  { -168.690067525980f,    -11.0958032831364f},
  { -153.434948822922f,    -12.6043826483792f},
  { -135.0f,    -13.2626760083048f},
  { -116.565051177078f,    -12.6043826483792f},
  { -101.309932474020f,    -11.0958032831364f},
  { -90.0f,    -9.46232220802562f},
  { -165.963756532074f,    -25.8766900608275f},
  { -146.309932474020f,    -29.0171406246015f},
  { -123.690067525980f,    -29.0171406246015f},
  { -104.036243467927f,    -25.8766900608275f},
  { -90.0f,    -21.8014094863518f},
  { -161.565051177078f,    -43.4915193450920f},
  { -135.0f,    -46.6861433417170f},
  { -108.434948822922f,    -43.4915193450920f},
  { -90.0f,    -36.8698976458440f},
  { -153.434948822922f,    -60.7940677526006f},
  { -116.565051177078f,    -60.7940677526006f},
  { -90.0f,    -53.1301023541560f},
  { -135.0f,    -74.2068309517360f},
  { -90.0f,    -68.1985905136482f},
  { -90.0f,    -80.5376777919744f},
  { -78.6900675259798f,    -11.0958032831364f},
  { -63.4349488229220f,    -12.6043826483792f},
  { -45.0f,    -13.2626760083048f},
  { -26.5650511770780f,    -12.6043826483792f},
  { -11.3099324740202f,    -11.0958032831364f},
  { -75.9637565320735f,    -25.8766900608275f},
  { -56.3099324740202f,    -29.0171406246015f},
  { -33.6900675259798f,    -29.0171406246015f},
  { -14.0362434679265f,    -25.8766900608275f},
  { -71.5650511770780f,    -43.4915193450920f},
  { -45.0f,    -46.6861433417170f},
  { -18.4349488229220f,    -43.4915193450920f},
  { -63.4349488229220f,    -60.7940677526006f},
  { -26.5650511770780f,    -60.7940677526006f},
  { -45.0f,    -74.2068309517360f}};
 
/* 3LD geosphere 'oct' [8 0] (258 points) */
const float __geosphere_oct_8_0_dirs_deg[258][2] =
{ { 0.0f,    0.0f},
  { 180.0f,    0.0f},
  { 90.0f,    0.0f},
  { -90.0f,    0.0f},
  { 0.0f,    90.0f},
  { 0.0f,    -90.0f},
  { 0.0f,    8.13010235415598f},
  { 0.0f,    18.4349488229220f},
  { 0.0f,    30.9637565320735f},
  { 0.0f,    45.0f},
  { 0.0f,    59.0362434679265f},
  { 0.0f,    71.5650511770780f},
  { 0.0f,    81.8698976458440f},
  { 8.13010235415598f,    0.0f},
  { 9.46232220802562f,    9.33585903200394f},
  { 11.3099324740202f,    21.4167140330336f},
  { 14.0362434679265f,    36.0398934303039f},
  { 18.4349488229220f,    51.6711818985441f},
  { 26.5650511770780f,    65.9051574478893f},
  { 45.0000000000000f,    76.7373239916952f},
  { 90.0f,    81.8698976458440f},
  { 18.4349488229220f,    0.0f},
  { 21.8014094863518f,    10.5197348906586f},
  { 26.5650511770780f,    24.0948425521107f},
  { 33.6900675259798f,    39.7621591518051f},
  { 45.0f,    54.7356103172453f},
  { 63.4349488229220f,    65.9051574478893f},
  { 90.0f,    71.5650511770780f},
  { 30.9637565320735f,    0.0f},
  { 36.8698976458440f,    11.3099324740202f},
  { 45.0000000000000f,    25.2394018206789f},
  { 56.3099324740202f,    39.7621591518051f},
  { 71.5650511770780f,    51.6711818985441f},
  { 90.0f,    59.0362434679265f},
  { 45.0f,    0.0f},
  { 53.1301023541560f,    11.3099324740202f},
  { 63.4349488229220f,    24.0948425521107f},
  { 75.9637565320735f,    36.0398934303039f},
  { 90.0f,    45.0f},
  { 59.0362434679265f,    0.0f},
  { 68.1985905136482f,    10.5197348906586f},
  { 78.6900675259798f,    21.4167140330336f},
  { 90.0f,    30.9637565320735f},
  { 71.5650511770780f,    0.0f},
  { 80.5376777919744f,    9.33585903200394f},
  { 90.0f,    18.4349488229220f},
  { 81.8698976458440f,    0.0f},
  { 90.0f,    8.13010235415598f},
  { 98.1301023541560f,    0.0f},
  { 99.4623222080256f,    9.33585903200394f},
  { 101.309932474020f,    21.4167140330336f},
  { 104.036243467927f,    36.0398934303039f},
  { 108.434948822922f,    51.6711818985441f},
  { 116.565051177078f,    65.9051574478893f},
  { 135.0f,    76.7373239916952f},
  { 180.0f,    81.8698976458440f},
  { 108.434948822922f,    0.0f},
  { 111.801409486352f,    10.5197348906586f},
  { 116.565051177078f,    24.0948425521107f},
  { 123.690067525980f,    39.7621591518051f},
  { 135.0f,    54.7356103172453f},
  { 153.434948822922f,    65.9051574478893f},
  { 180.0f,    71.5650511770780f},
  { 120.963756532074f,    0.0f},
  { 126.869897645844f,    11.3099324740202f},
  { 135.0f,    25.2394018206789f},
  { 146.309932474020f,    39.7621591518051f},
  { 161.565051177078f,    51.6711818985441f},
  { 180.0f,    59.0362434679265f},
  { 135.0f,    0.0f},
  { 143.130102354156f,    11.3099324740202f},
  { 153.434948822922f,    24.0948425521107f},
  { 165.963756532074f,    36.0398934303039f},
  { 180.0f,    45.0f},
  { 149.036243467926f,    0.0f},
  { 158.198590513648f,    10.5197348906586f},
  { 168.690067525980f,    21.4167140330336f},
  { 180.0f,    30.9637565320735f},
  { 161.565051177078f,    0.0f},
  { 170.537677791974f,    9.33585903200394f},
  { 180.0f,    18.4349488229220f},
  { 171.869897645844f,    0.0f},
  { 180.0f,    8.13010235415598f},
  { -171.869897645844f,    0.0f},
  { -170.537677791974f,    9.33585903200394f},
  { -168.690067525980f,    21.4167140330336f},
  { -165.963756532074f,    36.0398934303039f},
  { -161.565051177078f,    51.6711818985441f},
  { -153.434948822922f,    65.9051574478893f},
  { -135.0f,    76.7373239916952f},
  { -90.0f,    81.8698976458440f},
  { -161.565051177078f,    0.0f},
  { -158.198590513648f,    10.5197348906586f},
  { -153.434948822922f,    24.0948425521107f},
  { -146.309932474020f,    39.7621591518051f},
  { -135.0f,    54.7356103172453f},
  { -116.565051177078f,    65.9051574478893f},
  { -90.0f,    71.5650511770780f},
  { -149.036243467926f,    0.0f},
  { -143.130102354156f,    11.3099324740202f},
  { -135.0f,    25.2394018206789f},
  { -123.690067525980f,    39.7621591518051f},
  { -108.434948822922f,    51.6711818985441f},
  { -90.0f,    59.0362434679265f},
  { -135.0f,    0.0f},
  { -126.869897645844f,    11.3099324740202f},
  { -116.565051177078f,    24.0948425521107f},
  { -104.036243467927f,    36.0398934303039f},
  { -90.0f,    45.0f},
  { -120.963756532074f,    0.0f},
  { -111.801409486352f,    10.5197348906586f},
  { -101.309932474020f,    21.4167140330336f},
  { -90.0f,    30.9637565320735f},
  { -108.434948822922f,    0.0f},
  { -99.4623222080256f,    9.33585903200394f},
  { -90.0f,    18.4349488229220f},
  { -98.1301023541560f,    0.0f},
  { -90.0f,    8.13010235415598f},
  { -81.8698976458440f,    0.0f},
  { -80.5376777919744f,    9.33585903200394f},
  { -78.6900675259798f,    21.4167140330336f},
  { -75.9637565320735f,    36.0398934303039f},
  { -71.5650511770780f,    51.6711818985441f},
  { -63.4349488229220f,    65.9051574478893f},
  { -45.0000000000000f,    76.7373239916952f},
  { -71.5650511770780f,    0.0f},
  { -68.1985905136482f,    10.5197348906586f},
  { -63.4349488229220f,    24.0948425521107f},
  { -56.3099324740202f,    39.7621591518051f},
  { -45.0f,    54.7356103172453f},
  { -26.5650511770780f,    65.9051574478893f},
  { -59.0362434679265f,    0.0f},
  { -53.1301023541560f,    11.3099324740202f},
  { -45.0000000000000f,    25.2394018206789f},
  { -33.6900675259798f,    39.7621591518051f},
  { -18.4349488229220f,    51.6711818985441f},
  { -45.0f,    0.0f},
  { -36.8698976458440f,    11.3099324740202f},
  { -26.5650511770780f,    24.0948425521107f},
  { -14.0362434679265f,    36.0398934303039f},
  { -30.9637565320735f,    0.0f},
  { -21.8014094863518f,    10.5197348906586f},
  { -11.3099324740202f,    21.4167140330336f},
  { -18.4349488229220f,    0.0f},
  { -9.46232220802562f,    9.33585903200394f},
  { -8.13010235415598f,    0.0f},
  { 0.0f,    -8.13010235415598f},
  { 9.46232220802562f,    -9.33585903200394f},
  { 21.8014094863518f,    -10.5197348906586f},
  { 36.8698976458440f,    -11.3099324740202f},
  { 53.1301023541560f,    -11.3099324740202f},
  { 68.1985905136482f,    -10.5197348906586f},
  { 80.5376777919744f,    -9.33585903200394f},
  { 90.0f,    -8.13010235415598f},
  { 0.0f,    -18.4349488229220f},
  { 11.3099324740202f,    -21.4167140330336f},
  { 26.5650511770780f,    -24.0948425521107f},
  { 45.0000000000000f,    -25.2394018206789f},
  { 63.4349488229220f,    -24.0948425521107f},
  { 78.6900675259798f,    -21.4167140330336f},
  { 90.0f,    -18.4349488229220f},
  { 0.0f,    -30.9637565320735f},
  { 14.0362434679265f,    -36.0398934303039f},
  { 33.6900675259798f,    -39.7621591518051f},
  { 56.3099324740202f,    -39.7621591518051f},
  { 75.9637565320735f,    -36.0398934303039f},
  { 90.0f,    -30.9637565320735f},
  { 0.0f,    -45.0f},
  { 18.4349488229220f,    -51.6711818985441f},
  { 45.0f,    -54.7356103172453f},
  { 71.5650511770780f,    -51.6711818985441f},
  { 90.0f,    -45.0f},
  { 0.0f,    -59.0362434679265f},
  { 26.5650511770780f,    -65.9051574478893f},
  { 63.4349488229220f,    -65.9051574478893f},
  { 90.0f,    -59.0362434679265f},
  { 0.0f,    -71.5650511770780f},
  { 45.0000000000000f,    -76.7373239916952f},
  { 90.0f,    -71.5650511770780f},
  { 0.0f,    -81.8698976458440f},
  { 90.0f,    -81.8698976458440f},
  { 99.4623222080256f,    -9.33585903200394f},
  { 111.801409486352f,    -10.5197348906586f},
  { 126.869897645844f,    -11.3099324740202f},
  { 143.130102354156f,    -11.3099324740202f},
  { 158.198590513648f,    -10.5197348906586f},
  { 170.537677791974f,    -9.33585903200394f},
  { 180.0f,    -8.13010235415598f},
  { 101.309932474020f,    -21.4167140330336f},
  { 116.565051177078f,    -24.0948425521107f},
  { 135.0f,    -25.2394018206789f},
  { 153.434948822922f,    -24.0948425521107f},
  { 168.690067525980f,    -21.4167140330336f},
  { 180.0f,    -18.4349488229220f},
  { 104.036243467927f,    -36.0398934303039f},
  { 123.690067525980f,    -39.7621591518051f},
  { 146.309932474020f,    -39.7621591518051f},
  { 165.963756532074f,    -36.0398934303039f},
  { 180.0f,    -30.9637565320735f},
  { 108.434948822922f,    -51.6711818985441f},
  { 135.0f,    -54.7356103172453f},
  { 161.565051177078f,    -51.6711818985441f},
  { 180.0f,    -45.0f},
  { 116.565051177078f,    -65.9051574478893f},
  { 153.434948822922f,    -65.9051574478893f},
  { 180.0f,    -59.0362434679265f},
  { 135.0f,    -76.7373239916952f},
  { 180.0f,    -71.5650511770780f},
  { 180.0f,    -81.8698976458440f},
  { -170.537677791974f,    -9.33585903200394f},
  { -158.198590513648f,    -10.5197348906586f},
  { -143.130102354156f,    -11.3099324740202f},
  { -126.869897645844f,    -11.3099324740202f},
  { -111.801409486352f,    -10.5197348906586f},
  { -99.4623222080256f,    -9.33585903200394f},
  { -90.0f,    -8.13010235415598f},
  { -168.690067525980f,    -21.4167140330336f},
  { -153.434948822922f,    -24.0948425521107f},
  { -135.0f,    -25.2394018206789f},
  { -116.565051177078f,    -24.0948425521107f},
  { -101.309932474020f,    -21.4167140330336f},
  { -90.0f,    -18.4349488229220f},
  { -165.963756532074f,    -36.0398934303039f},
  { -146.309932474020f,    -39.7621591518051f},
  { -123.690067525980f,    -39.7621591518051f},
  { -104.036243467927f,    -36.0398934303039f},
  { -90.0f,    -30.9637565320735f},
  { -161.565051177078f,    -51.6711818985441f},
  { -135.0f,    -54.7356103172453f},
  { -108.434948822922f,    -51.6711818985441f},
  { -90.0f,    -45.0f},
  { -153.434948822922f,    -65.9051574478893f},
  { -116.565051177078f,    -65.9051574478893f},
  { -90.0f,    -59.0362434679265f},
  { -135.0f,    -76.7373239916952f},
  { -90.0f,    -71.5650511770780f},
  { -90.0f,    -81.8698976458440f},
  { -80.5376777919744f,    -9.33585903200394f},
  { -68.1985905136482f,    -10.5197348906586f},
  { -53.1301023541560f,    -11.3099324740202f},
  { -36.8698976458440f,    -11.3099324740202f},
  { -21.8014094863518f,    -10.5197348906586f},
  { -9.46232220802562f,    -9.33585903200394f},
  { -78.6900675259798f,    -21.4167140330336f},
  { -63.4349488229220f,    -24.0948425521107f},
  { -45.0000000000000f,    -25.2394018206789f},
  { -26.5650511770780f,    -24.0948425521107f},
  { -11.3099324740202f,    -21.4167140330336f},
  { -75.9637565320735f,    -36.0398934303039f},
  { -56.3099324740202f,    -39.7621591518051f},
  { -33.6900675259798f,    -39.7621591518051f},
  { -14.0362434679265f,    -36.0398934303039f},
  { -71.5650511770780f,    -51.6711818985441f},
  { -45.0f,    -54.7356103172453f},
  { -18.4349488229220f,    -51.6711818985441f},
  { -63.4349488229220f,    -65.9051574478893f},
  { -26.5650511770780f,    -65.9051574478893f},
  { -45.0000000000000f,    -76.7373239916952f}};
 
/* 3LD geosphere 'oct' [9 0] (326 points) */
const float __geosphere_oct_9_0_dirs_deg[326][2] =
{ { 0.0f,    0.0f},
  { 180.0f,    0.0f},
  { 90.0f,    0.0f},
  { -90.0f,    0.0f},
  { 0.0f,    90.0f},
  { 0.0f,    -90.0f},
  { 0.0f,    7.12501634890180f},
  { 0.0f,    15.9453959009229f},
  { 0.0f,    26.5650511770780f},
  { 0.0f,    38.6598082540901f},
  { 0.0f,    51.3401917459099f},
  { 0.0f,    63.4349488229220f},
  { 0.0f,    74.0546040990772f},
  { 0.0f,    82.8749836510982f},
  { 7.12501634890180f,    0.0f},
  { 8.13010235415598f,    8.04946697552840f},
  { 9.46232220802562f,    18.2007602645333f},
  { 11.3099324740202f,    30.4703594659797f},
  { 14.0362434679265f,    44.1317492120310f},
  { 18.4349488229220f,    57.6884667625762f},
  { 26.5650511770780f,    69.5606824267418f},
  { 45.0000000000000f,    78.5782463410377f},
  { 90.0f,    82.8749836510982f},
  { 15.9453959009229f,    0.0f},
  { 18.4349488229220f,    8.98487693168568f},
  { 21.8014094863518f,    20.3745271887352f},
  { 26.5650511770780f,    33.8545148126205f},
  { 33.6900675259798f,    47.9688862258027f},
  { 45.0f,    60.5037915034336f},
  { 63.4349488229220f,    69.5606824267418f},
  { 90.0f,    74.0546040990772f},
  { 26.5650511770780f,    0.0f},
  { 30.9637565320735f,    9.73147547315763f},
  { 36.8698976458440f,    21.8014094863518f},
  { 45.0000000000000f,    35.2643896827547f},
  { 56.3099324740202f,    47.9688862258027f},
  { 71.5650511770780f,    57.6884667625762f},
  { 90.0000000000000f,    63.4349488229220f},
  { 38.6598082540901f,    0.0f},
  { 45.0f,    10.0249878620757f},
  { 53.1301023541560f,    21.8014094863518f},
  { 63.4349488229220f,    33.8545148126205f},
  { 75.9637565320735f,    44.1317492120310f},
  { 90.0f,    51.3401917459099f},
  { 51.3401917459099f,    0.0f},
  { 59.0362434679265f,    9.73147547315763f},
  { 68.1985905136482f,    20.3745271887352f},
  { 78.6900675259798f,    30.4703594659797f},
  { 90.0f,    38.6598082540901f},
  { 63.4349488229220f,    0.0f},
  { 71.5650511770780f,    8.98487693168568f},
  { 80.5376777919744f,    18.2007602645333f},
  { 90.0f,    26.5650511770780f},
  { 74.0546040990772f,    0.0f},
  { 81.8698976458440f,    8.04946697552840f},
  { 90.0f,    15.9453959009229f},
  { 82.8749836510982f,    0.0f},
  { 90.0f,    7.12501634890180f},
  { 97.1250163489018f,    0.0f},
  { 98.1301023541560f,    8.04946697552840f},
  { 99.4623222080256f,    18.2007602645333f},
  { 101.309932474020f,    30.4703594659797f},
  { 104.036243467927f,    44.1317492120310f},
  { 108.434948822922f,    57.6884667625762f},
  { 116.565051177078f,    69.5606824267418f},
  { 135.0f,    78.5782463410377f},
  { 180.0f,    82.8749836510982f},
  { 105.945395900923f,    0.0f},
  { 108.434948822922f,    8.98487693168568f},
  { 111.801409486352f,    20.3745271887352f},
  { 116.565051177078f,    33.8545148126205f},
  { 123.690067525980f,    47.9688862258027f},
  { 135.0f,    60.5037915034336f},
  { 153.434948822922f,    69.5606824267418f},
  { 180.0f,    74.0546040990772f},
  { 116.565051177078f,    0.0f},
  { 120.963756532074f,    9.73147547315763f},
  { 126.869897645844f,    21.8014094863518f},
  { 135.0f,    35.2643896827547f},
  { 146.309932474020f,    47.9688862258027f},
  { 161.565051177078f,    57.6884667625762f},
  { 180.0f,    63.4349488229220f},
  { 128.659808254090f,    0.0f},
  { 135.0f,    10.0249878620757f},
  { 143.130102354156f,    21.8014094863518f},
  { 153.434948822922f,    33.8545148126205f},
  { 165.963756532074f,    44.1317492120310f},
  { 180.0f,    51.3401917459099f},
  { 141.340191745910f,    0.0f},
  { 149.036243467926f,    9.73147547315763f},
  { 158.198590513648f,    20.3745271887352f},
  { 168.690067525980f,    30.4703594659797f},
  { 180.0f,    38.6598082540901f},
  { 153.434948822922f,    0.0f},
  { 161.565051177078f,    8.98487693168568f},
  { 170.537677791974f,    18.2007602645333f},
  { 180.0f,    26.5650511770780f},
  { 164.054604099077f,    0.0f},
  { 171.869897645844f,    8.04946697552840f},
  { 180.0f,    15.9453959009229f},
  { 172.874983651098f,    0.0f},
  { 180.0f,    7.12501634890180f},
  { -172.874983651098f,    0.0f},
  { -171.869897645844f,    8.04946697552840f},
  { -170.537677791974f,    18.2007602645333f},
  { -168.690067525980f,    30.4703594659797f},
  { -165.963756532074f,    44.1317492120310f},
  { -161.565051177078f,    57.6884667625762f},
  { -153.434948822922f,    69.5606824267418f},
  { -135.000000000000f,    78.5782463410377f},
  { -90.0f,    82.8749836510982f},
  { -164.054604099077f,    0.0f},
  { -161.565051177078f,    8.98487693168568f},
  { -158.198590513648f,    20.3745271887352f},
  { -153.434948822922f,    33.8545148126205f},
  { -146.309932474020f,    47.9688862258027f},
  { -135.0f,    60.5037915034336f},
  { -116.565051177078f,    69.5606824267418f},
  { -90.0f,    74.0546040990772f},
  { -153.434948822922f,    0.0f},
  { -149.036243467926f,    9.73147547315763f},
  { -143.130102354156f,    21.8014094863518f},
  { -135.0f,    35.2643896827547f},
  { -123.690067525980f,    47.9688862258027f},
  { -108.434948822922f,    57.6884667625762f},
  { -90.0000000000000f,    63.4349488229220f},
  { -141.340191745910f,    0.0f},
  { -135.0f,    10.0249878620757f},
  { -126.869897645844f,    21.8014094863518f},
  { -116.565051177078f,    33.8545148126205f},
  { -104.036243467927f,    44.1317492120310f},
  { -90.0f,    51.3401917459099f},
  { -128.659808254090f,    0.0f},
  { -120.963756532074f,    9.73147547315763f},
  { -111.801409486352f,    20.3745271887352f},
  { -101.309932474020f,    30.4703594659797f},
  { -90.0f,    38.6598082540901f},
  { -116.565051177078f,    0.0f},
  { -108.434948822922f,    8.98487693168568f},
  { -99.4623222080256f,    18.2007602645333f},
  { -90.0000000000000f,    26.5650511770780f},
  { -105.945395900923f,    0.0f},
  { -98.1301023541560f,    8.04946697552840f},
  { -90.0f,    15.9453959009229f},
  { -97.1250163489018f,    0.0f},
  { -90.0f,    7.12501634890180f},
  { -82.8749836510982f,    0.0f},
  { -81.8698976458440f,    8.04946697552840f},
  { -80.5376777919744f,    18.2007602645333f},
  { -78.6900675259798f,    30.4703594659797f},
  { -75.9637565320735f,    44.1317492120310f},
  { -71.5650511770780f,    57.6884667625762f},
  { -63.4349488229220f,    69.5606824267418f},
  { -45.0000000000000f,    78.5782463410377f},
  { -74.0546040990772f,    0.0f},
  { -71.5650511770780f,    8.98487693168568f},
  { -68.1985905136482f,    20.3745271887352f},
  { -63.4349488229220f,    33.8545148126205f},
  { -56.3099324740202f,    47.9688862258027f},
  { -45.0f,    60.5037915034336f},
  { -26.5650511770780f,    69.5606824267418f},
  { -63.4349488229220f,    0.0f},
  { -59.0362434679265f,    9.73147547315763f},
  { -53.1301023541560f,    21.8014094863518f},
  { -45.0000000000000f,    35.2643896827547f},
  { -33.6900675259798f,    47.9688862258027f},
  { -18.4349488229220f,    57.6884667625762f},
  { -51.3401917459099f,    0.0f},
  { -45.0000000000000f,    10.0249878620757f},
  { -36.8698976458440f,    21.8014094863518f},
  { -26.5650511770780f,    33.8545148126205f},
  { -14.0362434679265f,    44.1317492120310f},
  { -38.6598082540901f,    0.0f},
  { -30.9637565320735f,    9.73147547315763f},
  { -21.8014094863518f,    20.3745271887352f},
  { -11.3099324740202f,    30.4703594659797f},
  { -26.5650511770780f,    0.0f},
  { -18.4349488229220f,    8.98487693168568f},
  { -9.46232220802562f,    18.2007602645333f},
  { -15.9453959009229f,    0.0f},
  { -8.13010235415598f,    8.04946697552840f},
  { -7.12501634890180f,    0.0f},
  { 0.0f,    -7.12501634890180f},
  { 8.13010235415598f,    -8.04946697552840f},
  { 18.4349488229220f,    -8.98487693168568f},
  { 30.9637565320735f,    -9.73147547315763f},
  { 45.0f,    -10.0249878620757f},
  { 59.0362434679265f,    -9.73147547315763f},
  { 71.5650511770780f,    -8.98487693168568f},
  { 81.8698976458440f,    -8.04946697552840f},
  { 90.0f,    -7.12501634890180f},
  { 0.0f,    -15.9453959009229f},
  { 9.46232220802562f,    -18.2007602645333f},
  { 21.8014094863518f,    -20.3745271887352f},
  { 36.8698976458440f,    -21.8014094863518f},
  { 53.1301023541560f,    -21.8014094863518f},
  { 68.1985905136482f,    -20.3745271887352f},
  { 80.5376777919744f,    -18.2007602645333f},
  { 90.0f,    -15.9453959009229f},
  { 0.0f,    -26.5650511770780f},
  { 11.3099324740202f,    -30.4703594659797f},
  { 26.5650511770780f,    -33.8545148126205f},
  { 45.0000000000000f,    -35.2643896827547f},
  { 63.4349488229220f,    -33.8545148126205f},
  { 78.6900675259798f,    -30.4703594659797f},
  { 90.0f,    -26.5650511770780f},
  { 0.0f,    -38.6598082540901f},
  { 14.0362434679265f,    -44.1317492120310f},
  { 33.6900675259798f,    -47.9688862258027f},
  { 56.3099324740202f,    -47.9688862258027f},
  { 75.9637565320735f,    -44.1317492120310f},
  { 90.0f,    -38.6598082540901f},
  { 0.0f,    -51.3401917459099f},
  { 18.4349488229220f,    -57.6884667625762f},
  { 45.0f,    -60.5037915034336f},
  { 71.5650511770780f,    -57.6884667625762f},
  { 90.0f,    -51.3401917459099f},
  { 0.0f,    -63.4349488229220f},
  { 26.5650511770780f,    -69.5606824267418f},
  { 63.4349488229220f,    -69.5606824267418f},
  { 90.0f,    -63.4349488229220f},
  { 0.0f,    -74.0546040990772f},
  { 45.0f,    -78.5782463410377f},
  { 90.0f,    -74.0546040990772f},
  { 0.0f,    -82.8749836510982f},
  { 90.0f,    -82.8749836510982f},
  { 98.1301023541560f,    -8.04946697552840f},
  { 108.434948822922f,    -8.98487693168568f},
  { 120.963756532074f,    -9.73147547315763f},
  { 135.0f,    -10.0249878620757f},
  { 149.036243467926f,    -9.73147547315763f},
  { 161.565051177078f,    -8.98487693168568f},
  { 171.869897645844f,    -8.04946697552840f},
  { 180.0f,    -7.12501634890180f},
  { 99.4623222080256f,    -18.2007602645333f},
  { 111.801409486352f,    -20.3745271887352f},
  { 126.869897645844f,    -21.8014094863518f},
  { 143.130102354156f,    -21.8014094863518f},
  { 158.198590513648f,    -20.3745271887352f},
  { 170.537677791974f,    -18.2007602645333f},
  { 180.0f,    -15.9453959009229f},
  { 101.309932474020f,    -30.4703594659797f},
  { 116.565051177078f,    -33.8545148126205f},
  { 135.0f,    -35.2643896827547f},
  { 153.434948822922f,    -33.8545148126205f},
  { 168.690067525980f,    -30.4703594659797f},
  { 180.0f,    -26.5650511770780f},
  { 104.036243467927f,    -44.1317492120310f},
  { 123.690067525980f,    -47.9688862258027f},
  { 146.309932474020f,    -47.9688862258027f},
  { 165.963756532074f,    -44.1317492120310f},
  { 180.0f,    -38.6598082540901f},
  { 108.434948822922f,    -57.6884667625762f},
  { 135.0f,    -60.5037915034336f},
  { 161.565051177078f,    -57.6884667625762f},
  { 180.0f,    -51.3401917459099f},
  { 116.565051177078f,    -69.5606824267418f},
  { 153.434948822922f,    -69.5606824267418f},
  { 180.0f,    -63.4349488229220f},
  { 135.0f,    -78.5782463410377f},
  { 180.0f,    -74.0546040990772f},
  { 180.0f,    -82.8749836510982f},
  { -171.869897645844f,    -8.04946697552840f},
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  { -149.036243467926f,    -9.73147547315763f},
  { -135.0f,    -10.0249878620757f},
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  { -90.0f,    -7.12501634890180f},
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  { -90.0f,    -15.9453959009229f},
  { -168.690067525980f,    -30.4703594659797f},
  { -153.434948822922f,    -33.8545148126205f},
  { -135.0f,    -35.2643896827547f},
  { -116.565051177078f,    -33.8545148126205f},
  { -101.309932474020f,    -30.4703594659797f},
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  { -14.0362434679265f,    -44.1317492120310f},
  { -71.5650511770780f,    -57.6884667625762f},
  { -45.0f,    -60.5037915034336f},
  { -18.4349488229220f,    -57.6884667625762f},
  { -63.4349488229220f,    -69.5606824267418f},
  { -26.5650511770780f,    -69.5606824267418f},
  { -45.0f,    -78.5782463410377f}};
 
/* 3LD geosphere 'oct' [10 0] (402 points) */
const float __geosphere_oct_10_0_dirs_deg[402][2] =
{ { 0.0f,    0.0f},
  { 180.0f,    0.0f},
  { 90.0f,    0.0f},
  { -90.0f,    0.0f},
  { 0.0f,    90.0f},
  { 0.0f,    -90.0f},
  { 0.0f,    6.34019174590991f},
  { 0.0f,    14.0362434679265f},
  { 0.0f,    23.1985905136482f},
  { 0.0f,    33.6900675259798f},
  { 0.0f,    45.0f},
  { 0.0f,    56.3099324740202f},
  { 0.0f,    66.8014094863518f},
  { 0.0f,    75.9637565320735f},
  { 0.0f,    83.6598082540901f},
  { 6.34019174590991f,    0.0f},
  { 7.12501634890180f,    7.07055511696583f},
  { 8.13010235415598f,    15.7931690482640f},
  { 9.46232220802562f,    26.2523751177207f},
  { 11.3099324740202f,    38.1129265009866f},
  { 14.0362434679265f,    50.4902877138061f},
  { 18.4349488229220f,    62.2086943552208f},
  { 26.5650511770780f,    72.2845276563321f},
  { 45.0000000000000f,    79.9750121379243f},
  { 89.9999999999999f,    83.6598082540901f},
  { 14.0362434679265f,    0.0f},
  { 15.9453959009229f,    7.82123550649965f},
  { 18.4349488229220f,    17.5484006137923f},
  { 21.8014094863518f,    29.1215680703514f},
  { 26.5650511770780f,    41.8103148957786f},
  { 33.6900675259798f,    54.2042400852929f},
  { 45.0f,    64.7605981793211f},
  { 63.4349488229220f,    72.2845276563321f},
  { 90.0f,    75.9637565320735f},
  { 23.1985905136482f,    0.0f},
  { 26.5650511770780f,    8.47871314708616f},
  { 30.9637565320735f,    18.9318231808652f},
  { 36.8698976458440f,    30.9637565320735f},
  { 45.0000000000000f,    43.3138566582830f},
  { 56.3099324740202f,    54.2042400852929f},
  { 71.5650511770780f,    62.2086943552208f},
  { 90.0f,    66.8014094863518f},
  { 33.6900675259798f,    0.0f},
  { 38.6598082540901f,    8.87639508097334f},
  { 45.0f,    19.4712206344907f},
  { 53.1301023541560f,    30.9637565320735f},
  { 63.4349488229220f,    41.8103148957786f},
  { 75.9637565320735f,    50.4902877138061f},
  { 90.0f,    56.3099324740202f},
  { 45.0f,    0.0f},
  { 51.3401917459099f,    8.87639508097334f},
  { 59.0362434679265f,    18.9318231808652f},
  { 68.1985905136482f,    29.1215680703514f},
  { 78.6900675259798f,    38.1129265009866f},
  { 90.0f,    45.0f},
  { 56.3099324740202f,    0.0f},
  { 63.4349488229220f,    8.47871314708616f},
  { 71.5650511770780f,    17.5484006137923f},
  { 80.5376777919744f,    26.2523751177207f},
  { 90.0f,    33.6900675259798f},
  { 66.8014094863518f,    0.0f},
  { 74.0546040990771f,    7.82123550649965f},
  { 81.8698976458440f,    15.7931690482640f},
  { 90.0f,    23.1985905136482f},
  { 75.9637565320735f,    0.0f},
  { 82.8749836510982f,    7.07055511696583f},
  { 90.0f,    14.0362434679265f},
  { 83.6598082540901f,    0.0f},
  { 90.0f,    6.34019174590991f},
  { 96.3401917459099f,    0.0f},
  { 97.1250163489018f,    7.07055511696583f},
  { 98.1301023541560f,    15.7931690482640f},
  { 99.4623222080256f,    26.2523751177207f},
  { 101.309932474020f,    38.1129265009866f},
  { 104.036243467927f,    50.4902877138061f},
  { 108.434948822922f,    62.2086943552208f},
  { 116.565051177078f,    72.2845276563321f},
  { 135.0f,    79.9750121379243f},
  { 180.000000000000f,    83.6598082540901f},
  { 104.036243467927f,    0.0f},
  { 105.945395900923f,    7.82123550649965f},
  { 108.434948822922f,    17.5484006137923f},
  { 111.801409486352f,    29.1215680703514f},
  { 116.565051177078f,    41.8103148957786f},
  { 123.690067525980f,    54.2042400852929f},
  { 135.0f,    64.7605981793211f},
  { 153.434948822922f,    72.2845276563321f},
  { 180.0f,    75.9637565320735f},
  { 113.198590513648f,    0.0f},
  { 116.565051177078f,    8.47871314708616f},
  { 120.963756532074f,    18.9318231808652f},
  { 126.869897645844f,    30.9637565320735f},
  { 135.0f,    43.3138566582830f},
  { 146.309932474020f,    54.2042400852929f},
  { 161.565051177078f,    62.2086943552208f},
  { 180.0f,    66.8014094863518f},
  { 123.690067525980f,    0.0f},
  { 128.659808254090f,    8.87639508097334f},
  { 135.0f,    19.4712206344907f},
  { 143.130102354156f,    30.9637565320735f},
  { 153.434948822922f,    41.8103148957786f},
  { 165.963756532074f,    50.4902877138061f},
  { 180.0f,    56.3099324740202f},
  { 135.0f,    0.0f},
  { 141.340191745910f,    8.87639508097334f},
  { 149.036243467926f,    18.9318231808652f},
  { 158.198590513648f,    29.1215680703514f},
  { 168.690067525980f,    38.1129265009866f},
  { 180.0f,    45.0f},
  { 146.309932474020f,    0.0f},
  { 153.434948822922f,    8.47871314708616f},
  { 161.565051177078f,    17.5484006137923f},
  { 170.537677791974f,    26.2523751177207f},
  { 180.0f,    33.6900675259798f},
  { 156.801409486352f,    0.0f},
  { 164.054604099077f,    7.82123550649965f},
  { 171.869897645844f,    15.7931690482640f},
  { 180.0f,    23.1985905136482f},
  { 165.963756532074f,    0.0f},
  { 172.874983651098f,    7.07055511696583f},
  { 180.0f,    14.0362434679265f},
  { 173.659808254090f,    0.0f},
  { 180.0f,    6.34019174590991f},
  { -173.659808254090f,    0.0f},
  { -172.874983651098f,    7.07055511696583f},
  { -171.869897645844f,    15.7931690482640f},
  { -170.537677791974f,    26.2523751177207f},
  { -168.690067525980f,    38.1129265009866f},
  { -165.963756532074f,    50.4902877138061f},
  { -161.565051177078f,    62.2086943552208f},
  { -153.434948822922f,    72.2845276563321f},
  { -135.0f,    79.9750121379243f},
  { -90.0000000000001f,    83.6598082540901f},
  { -165.963756532074f,    0.0f},
  { -164.054604099077f,    7.82123550649965f},
  { -161.565051177078f,    17.5484006137923f},
  { -158.198590513648f,    29.1215680703514f},
  { -153.434948822922f,    41.8103148957786f},
  { -146.309932474020f,    54.2042400852929f},
  { -135.0f,    64.7605981793211f},
  { -116.565051177078f,    72.2845276563321f},
  { -90.0f,    75.9637565320735f},
  { -156.801409486352f,    0.0f},
  { -153.434948822922f,    8.47871314708616f},
  { -149.036243467926f,    18.9318231808652f},
  { -143.130102354156f,    30.9637565320735f},
  { -135.0f,    43.3138566582830f},
  { -123.690067525980f,    54.2042400852929f},
  { -108.434948822922f,    62.2086943552208f},
  { -90.0f,    66.8014094863518f},
  { -146.309932474020f,    0.0f},
  { -141.340191745910f,    8.87639508097334f},
  { -135.0f,    19.4712206344907f},
  { -126.869897645844f,    30.9637565320735f},
  { -116.565051177078f,    41.8103148957786f},
  { -104.036243467927f,    50.4902877138061f},
  { -90.0f,    56.3099324740202f},
  { -135.0f,    0.0f},
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  { -120.963756532074f,    18.9318231808652f},
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  { -101.309932474020f,    38.1129265009866f},
  { -90.0f,    45.0f},
  { -123.690067525980f,    0.0f},
  { -116.565051177078f,    8.47871314708616f},
  { -108.434948822922f,    17.5484006137923f},
  { -99.4623222080256f,    26.2523751177207f},
  { -90.0f,    33.6900675259798f},
  { -113.198590513648f,    0.0f},
  { -105.945395900923f,    7.82123550649965f},
  { -98.1301023541560f,    15.7931690482640f},
  { -90.0f,    23.1985905136482f},
  { -104.036243467927f,    0.0f},
  { -97.1250163489018f,    7.07055511696582f},
  { -90.0f,    14.0362434679265f},
  { -96.3401917459099f,    0.0f},
  { -90.0f,    6.34019174590991f},
  { -83.6598082540901f,    0.0f},
  { -82.8749836510982f,    7.07055511696583f},
  { -81.8698976458440f,    15.7931690482640f},
  { -80.5376777919744f,    26.2523751177207f},
  { -78.6900675259798f,    38.1129265009866f},
  { -75.9637565320735f,    50.4902877138061f},
  { -71.5650511770780f,    62.2086943552208f},
  { -63.4349488229220f,    72.2845276563321f},
  { -45.0000000000000f,    79.9750121379243f},
  { -75.9637565320735f,    0.0f},
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  { -71.5650511770780f,    17.5484006137923f},
  { -68.1985905136482f,    29.1215680703514f},
  { -63.4349488229220f,    41.8103148957786f},
  { -56.3099324740202f,    54.2042400852929f},
  { -45.0000000000000f,    64.7605981793211f},
  { -26.5650511770780f,    72.2845276563321f},
  { -66.8014094863518f,    0.0f},
  { -63.4349488229220f,    8.47871314708616f},
  { -59.0362434679265f,    18.9318231808652f},
  { -53.1301023541560f,    30.9637565320735f},
  { -45.0000000000000f,    43.3138566582830f},
  { -33.6900675259798f,    54.2042400852929f},
  { -18.4349488229220f,    62.2086943552208f},
  { -56.3099324740202f,    0.0f},
  { -51.3401917459099f,    8.87639508097334f},
  { -45.0f,    19.4712206344907f},
  { -36.8698976458440f,    30.9637565320735f},
  { -26.5650511770780f,    41.8103148957786f},
  { -14.0362434679265f,    50.4902877138061f},
  { -45.0f,    0.0f},
  { -38.6598082540901f,    8.87639508097334f},
  { -30.9637565320735f,    18.9318231808652f},
  { -21.8014094863518f,    29.1215680703514f},
  { -11.3099324740202f,    38.1129265009866f},
  { -33.6900675259798f,    0.0f},
  { -26.5650511770780f,    8.47871314708616f},
  { -18.4349488229220f,    17.5484006137923f},
  { -9.46232220802562f,    26.2523751177207f},
  { -23.1985905136482f,    0.0f},
  { -15.9453959009229f,    7.82123550649965f},
  { -8.13010235415598f,    15.7931690482640f},
  { -14.0362434679265f,    0.0f},
  { -7.12501634890180f,    7.07055511696582f},
  { -6.34019174590991f,    0.0f},
  { 0.0f,    -6.34019174590991f},
  { 7.12501634890180f,    -7.07055511696583f},
  { 15.9453959009229f,    -7.82123550649965f},
  { 26.5650511770780f,    -8.47871314708616f},
  { 38.6598082540901f,    -8.87639508097334f},
  { 51.3401917459099f,    -8.87639508097334f},
  { 63.4349488229220f,    -8.47871314708616f},
  { 74.0546040990771f,    -7.82123550649965f},
  { 82.8749836510982f,    -7.07055511696583f},
  { 90.0f,    -6.34019174590991f},
  { 0.0f,    -14.0362434679265f},
  { 8.13010235415598f,    -15.7931690482640f},
  { 18.4349488229220f,    -17.5484006137923f},
  { 30.9637565320735f,    -18.9318231808652f},
  { 45.0f,    -19.4712206344907f},
  { 59.0362434679265f,    -18.9318231808652f},
  { 71.5650511770780f,    -17.5484006137923f},
  { 81.8698976458440f,    -15.7931690482640f},
  { 90.0f,    -14.0362434679265f},
  { 0.0f,    -23.1985905136482f},
  { 9.46232220802562f,    -26.2523751177207f},
  { 21.8014094863518f,    -29.1215680703514f},
  { 36.8698976458440f,    -30.9637565320735f},
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  { 68.1985905136482f,    -29.1215680703514f},
  { 80.5376777919744f,    -26.2523751177207f},
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  { 26.5650511770780f,    -41.8103148957786f},
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  { 63.4349488229220f,    -41.8103148957786f},
  { 78.6900675259798f,    -38.1129265009866f},
  { 90.0f,    -33.6900675259798f},
  { 0.0f,    -45.0f},
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  { 33.6900675259798f,    -54.2042400852929f},
  { 56.3099324740202f,    -54.2042400852929f},
  { 75.9637565320735f,    -50.4902877138061f},
  { 90.0f,    -45.0f},
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  { 18.4349488229220f,    -62.2086943552208f},
  { 45.0f,    -64.7605981793211f},
  { 71.5650511770780f,    -62.2086943552208f},
  { 90.0f,    -56.3099324740202f},
  { 0.0f,    -66.8014094863518f},
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  { 63.4349488229220f,    -72.2845276563321f},
  { 90.0f,    -66.8014094863518f},
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  { 90.0f,    -75.9637565320735f},
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  { 90.0f,    -83.6598082540901f},
  { 97.1250163489018f,    -7.07055511696583f},
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  { 116.565051177078f,    -8.47871314708616f},
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  { 161.565051177078f,    -17.5484006137923f},
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  { 180.0f,    -45.0f},
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  { -135.0f,    -43.3138566582831f},
  { -116.565051177078f,    -41.8103148957786f},
  { -101.309932474020f,    -38.1129265009866f},
  { -90.0f,    -33.6900675259798f},
  { -165.963756532074f,    -50.4902877138061f},
  { -146.309932474020f,    -54.2042400852929f},
  { -123.690067525980f,    -54.2042400852929f},
  { -104.036243467927f,    -50.4902877138061f},
  { -90.0f,    -45.0f},
  { -161.565051177078f,    -62.2086943552208f},
  { -135.0f,    -64.7605981793211f},
  { -108.434948822922f,    -62.2086943552208f},
  { -90.0f,    -56.3099324740202f},
  { -153.434948822922f,    -72.2845276563321f},
  { -116.565051177078f,    -72.2845276563321f},
  { -90.0f,    -66.8014094863518f},
  { -135.0f,    -79.9750121379243f},
  { -90.0f,    -75.9637565320735f},
  { -90.0f,    -83.6598082540901f},
  { -82.8749836510982f,    -7.07055511696583f},
  { -74.0546040990771f,    -7.82123550649965f},
  { -63.4349488229220f,    -8.47871314708616f},
  { -51.3401917459099f,    -8.87639508097334f},
  { -38.6598082540901f,    -8.87639508097334f},
  { -26.5650511770780f,    -8.47871314708616f},
  { -15.9453959009229f,    -7.82123550649965f},
  { -7.12501634890180f,    -7.07055511696583f},
  { -81.8698976458440f,    -15.7931690482640f},
  { -71.5650511770780f,    -17.5484006137923f},
  { -59.0362434679265f,    -18.9318231808652f},
  { -45.0f,    -19.4712206344907f},
  { -30.9637565320735f,    -18.9318231808652f},
  { -18.4349488229220f,    -17.5484006137923f},
  { -8.13010235415598f,    -15.7931690482640f},
  { -80.5376777919744f,    -26.2523751177207f},
  { -68.1985905136482f,    -29.1215680703514f},
  { -53.1301023541560f,    -30.9637565320735f},
  { -36.8698976458440f,    -30.9637565320735f},
  { -21.8014094863518f,    -29.1215680703514f},
  { -9.46232220802563f,    -26.2523751177207f},
  { -78.6900675259798f,    -38.1129265009866f},
  { -63.4349488229220f,    -41.8103148957786f},
  { -45.0000000000000f,    -43.3138566582831f},
  { -26.5650511770780f,    -41.8103148957786f},
  { -11.3099324740202f,    -38.1129265009866f},
  { -75.9637565320735f,    -50.4902877138061f},
  { -56.3099324740202f,    -54.2042400852929f},
  { -33.6900675259798f,    -54.2042400852929f},
  { -14.0362434679265f,    -50.4902877138061f},
  { -71.5650511770780f,    -62.2086943552208f},
  { -45.0f,    -64.7605981793211f},
  { -18.4349488229220f,    -62.2086943552208f},
  { -63.4349488229220f,    -72.2845276563321f},
  { -26.5650511770780f,    -72.2845276563321f},
  { -45.0000000000000f,    -79.9750121379243f}};
 
/* 3LD geosphere 'oct' [11 0] (486 points) */
const float __geosphere_oct_11_0_dirs_deg[486][2] =
{ { 0.0f,    0.0f},
  { 180.0f,    0.0f},
  { 90.0f,    0.0f},
  { -90.0f,    0.0f},
  { 0.0f,    90.0f},
  { 0.0f,    -90.0f},
  { 0.0f,    5.71059313749964f},
  { 0.0f,    12.5288077091515f},
  { 0.0f,    20.5560452195835f},
  { 0.0f,    29.7448812969422f},
  { 0.0f,    39.8055710922652f},
  { 0.0f,    50.1944289077348f},
  { 0.0f,    60.2551187030578f},
  { 0.0f,    69.4439547804165f},
  { 0.0f,    77.4711922908485f},
  { 0.0f,    84.2894068625003f},
  { 5.71059313749964f,    0.0f},
  { 6.34019174590991f,    6.30172637399719f},
  { 7.12501634890180f,    13.9320915492581f},
  { 8.13010235415598f,    22.9897677736088f},
  { 9.46232220802562f,    33.3287577974902f},
  { 11.3099324740202f,    44.4382406711498f},
  { 14.0362434679265f,    55.5037627099091f},
  { 18.4349488229220f,    65.6887386511478f},
  { 26.5650511770780f,    74.3838705949755f},
  { 45.0000000000000f,    81.0698581640985f},
  { 89.9999999999999f,    84.2894068625003f},
  { 12.5288077091515f,    0.0f},
  { 14.0362434679265f,    6.91437177215212f},
  { 15.9453959009229f,    15.3613953897309f},
  { 18.4349488229220f,    25.3769335251523f},
  { 21.8014094863518f,    36.6042764427057f},
  { 26.5650511770780f,    48.1896851042214f},
  { 33.6900675259798f,    58.9972808661260f},
  { 45.0000000000000f,    67.9982863255502f},
  { 63.4349488229220f,    74.3838705949755f},
  { 90.0f,    77.4711922908485f},
  { 20.5560452195835f,    0.0f},
  { 23.1985905136482f,    7.48050889170827f},
  { 26.5650511770780f,    16.6015495990202f},
  { 30.9637565320735f,    27.2256279985640f},
  { 36.8698976458440f,    38.6598082540901f},
  { 45.0000000000000f,    49.6844577892274f},
  { 56.3099324740202f,    58.9972808661260f},
  { 71.5650511770780f,    65.6887386511478f},
  { 90.0f,    69.4439547804165f},
  { 29.7448812969422f,    0.0f},
  { 33.6900675259798f,    7.89514210504579f},
  { 38.6598082540901f,    17.3460652926699f},
  { 45.0000000000000f,    27.9383527296024f},
  { 53.1301023541560f,    38.6598082540901f},
  { 63.4349488229220f,    48.1896851042214f},
  { 75.9637565320736f,    55.5037627099091f},
  { 90.0f,    60.2551187030578f},
  { 39.8055710922652f,    0.0f},
  { 45.0f,    8.04946697552840f},
  { 51.3401917459099f,    17.3460652926699f},
  { 59.0362434679265f,    27.2256279985640f},
  { 68.1985905136482f,    36.6042764427057f},
  { 78.6900675259798f,    44.4382406711498f},
  { 90.0f,    50.1944289077348f},
  { 50.1944289077348f,    0.0f},
  { 56.3099324740202f,    7.89514210504579f},
  { 63.4349488229220f,    16.6015495990202f},
  { 71.5650511770780f,    25.3769335251523f},
  { 80.5376777919744f,    33.3287577974902f},
  { 90.0f,    39.8055710922652f},
  { 60.2551187030578f,    0.0f},
  { 66.8014094863518f,    7.48050889170827f},
  { 74.0546040990772f,    15.3613953897309f},
  { 81.8698976458440f,    22.9897677736088f},
  { 90.0f,    29.7448812969422f},
  { 69.4439547804165f,    0.0f},
  { 75.9637565320735f,    6.91437177215212f},
  { 82.8749836510982f,    13.9320915492581f},
  { 90.0f,    20.5560452195835f},
  { 77.4711922908485f,    0.0f},
  { 83.6598082540901f,    6.30172637399719f},
  { 90.0f,    12.5288077091515f},
  { 84.2894068625003f,    0.0f},
  { 90.0f,    5.71059313749965f},
  { 95.7105931374996f,    0.0f},
  { 96.3401917459099f,    6.30172637399719f},
  { 97.1250163489018f,    13.9320915492581f},
  { 98.1301023541560f,    22.9897677736088f},
  { 99.4623222080256f,    33.3287577974902f},
  { 101.309932474020f,    44.4382406711498f},
  { 104.036243467927f,    55.5037627099091f},
  { 108.434948822922f,    65.6887386511478f},
  { 116.565051177078f,    74.3838705949755f},
  { 135.0f,    81.0698581640985f},
  { 180.000000000000f,    84.2894068625003f},
  { 102.528807709152f,    0.0f},
  { 104.036243467927f,    6.91437177215212f},
  { 105.945395900923f,    15.3613953897309f},
  { 108.434948822922f,    25.3769335251523f},
  { 111.801409486352f,    36.6042764427057f},
  { 116.565051177078f,    48.1896851042214f},
  { 123.690067525980f,    58.9972808661260f},
  { 135.0f,    67.9982863255502f},
  { 153.434948822922f,    74.3838705949755f},
  { 180.0f,    77.4711922908485f},
  { 110.556045219583f,    0.0f},
  { 113.198590513648f,    7.48050889170827f},
  { 116.565051177078f,    16.6015495990202f},
  { 120.963756532074f,    27.2256279985640f},
  { 126.869897645844f,    38.6598082540901f},
  { 135.0f,    49.6844577892274f},
  { 146.309932474020f,    58.9972808661260f},
  { 161.565051177078f,    65.6887386511478f},
  { 180.0f,    69.4439547804165f},
  { 119.744881296942f,    0.0f},
  { 123.690067525980f,    7.89514210504579f},
  { 128.659808254090f,    17.3460652926699f},
  { 135.0f,    27.9383527296024f},
  { 143.130102354156f,    38.6598082540901f},
  { 153.434948822922f,    48.1896851042214f},
  { 165.963756532074f,    55.5037627099091f},
  { 180.0f,    60.2551187030578f},
  { 129.805571092265f,    0.0f},
  { 135.0f,    8.04946697552840f},
  { 141.340191745910f,    17.3460652926699f},
  { 149.036243467926f,    27.2256279985640f},
  { 158.198590513648f,    36.6042764427057f},
  { 168.690067525980f,    44.4382406711498f},
  { 180.0f,    50.1944289077348f},
  { 140.194428907735f,    0.0f},
  { 146.309932474020f,    7.89514210504579f},
  { 153.434948822922f,    16.6015495990202f},
  { 161.565051177078f,    25.3769335251523f},
  { 170.537677791974f,    33.3287577974902f},
  { 180.0f,    39.8055710922652f},
  { 150.255118703058f,    0.0f},
  { 156.801409486352f,    7.48050889170827f},
  { 164.054604099077f,    15.3613953897309f},
  { 171.869897645844f,    22.9897677736088f},
  { 180.0f,    29.7448812969422f},
  { 159.443954780417f,    0.0f},
  { 165.963756532074f,    6.91437177215212f},
  { 172.874983651098f,    13.9320915492581f},
  { 180.0f,    20.5560452195835f},
  { 167.471192290848f,    0.0f},
  { 173.659808254090f,    6.30172637399719f},
  { 180.0f,    12.5288077091515f},
  { 174.289406862500f,    0.0f},
  { 180.0f,    5.71059313749965f},
  { -174.289406862500f,    0.0f},
  { -173.659808254090f,    6.30172637399719f},
  { -172.874983651098f,    13.9320915492581f},
  { -171.869897645844f,    22.9897677736088f},
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  { -135.0f,    81.0698581640985f},
  { -90.0000000000001f,    84.2894068625003f},
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  { -153.434948822922f,    48.1896851042214f},
  { -146.309932474020f,    58.9972808661260f},
  { -135.0f,    67.9982863255502f},
  { -116.565051177078f,    74.3838705949755f},
  { -90.0f,    77.4711922908485f},
  { -159.443954780417f,    0.0f},
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  { -153.434948822922f,    16.6015495990202f},
  { -149.036243467926f,    27.2256279985640f},
  { -143.130102354156f,    38.6598082540901f},
  { -135.0f,    49.6844577892274f},
  { -123.690067525980f,    58.9972808661260f},
  { -108.434948822922f,    65.6887386511478f},
  { -90.0f,    69.4439547804165f},
  { -150.255118703058f,    0.0f},
  { -146.309932474020f,    7.89514210504579f},
  { -141.340191745910f,    17.3460652926699f},
  { -135.0f,    27.9383527296024f},
  { -126.869897645844f,    38.6598082540901f},
  { -116.565051177078f,    48.1896851042214f},
  { -104.036243467926f,    55.5037627099091f},
  { -90.0f,    60.2551187030578f},
  { -140.194428907735f,    0.0f},
  { -135.0f,    8.04946697552840f},
  { -128.659808254090f,    17.3460652926699f},
  { -120.963756532074f,    27.2256279985640f},
  { -111.801409486352f,    36.6042764427057f},
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  { -90.0f,    50.1944289077348f},
  { -129.805571092265f,    0.0f},
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  { -116.565051177078f,    16.6015495990202f},
  { -108.434948822922f,    25.3769335251523f},
  { -99.4623222080256f,    33.3287577974902f},
  { -90.0f,    39.8055710922652f},
  { -119.744881296942f,    0.0f},
  { -113.198590513648f,    7.48050889170827f},
  { -105.945395900923f,    15.3613953897309f},
  { -98.1301023541560f,    22.9897677736088f},
  { -90.0f,    29.7448812969422f},
  { -110.556045219583f,    0.0f},
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  { -63.4349488229220f,    16.6015495990202f},
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  { -36.8698976458440f,    38.6598082540901f},
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  { 83.6598082540901f,    -6.30172637399719f},
  { 90.0f,    -5.71059313749965f},
  { 0.0f,    -12.5288077091515f},
  { 7.12501634890180f,    -13.9320915492581f},
  { 15.9453959009229f,    -15.3613953897309f},
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  { 74.0546040990771f,    -15.3613953897309f},
  { 82.8749836510982f,    -13.9320915492581f},
  { 90.0f,    -12.5288077091515f},
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  { 18.4349488229220f,    -25.3769335251523f},
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  { 71.5650511770780f,    -25.3769335251523f},
  { 81.8698976458440f,    -22.9897677736088f},
  { 90.0f,    -20.5560452195835f},
  { 0.0f,    -29.7448812969422f},
  { 9.46232220802562f,    -33.3287577974902f},
  { 21.8014094863518f,    -36.6042764427057f},
  { 36.8698976458440f,    -38.6598082540901f},
  { 53.1301023541560f,    -38.6598082540901f},
  { 68.1985905136482f,    -36.6042764427057f},
  { 80.5376777919744f,    -33.3287577974902f},
  { 90.0f,    -29.7448812969422f},
  { 0.0f,    -39.8055710922652f},
  { 11.3099324740202f,    -44.4382406711498f},
  { 26.5650511770780f,    -48.1896851042214f},
  { 45.0f,    -49.6844577892274f},
  { 63.4349488229220f,    -48.1896851042214f},
  { 78.6900675259798f,    -44.4382406711498f},
  { 90.0f,    -39.8055710922652f},
  { 0.0f,    -50.1944289077348f},
  { 14.0362434679265f,    -55.5037627099091f},
  { 33.6900675259798f,    -58.9972808661260f},
  { 56.3099324740202f,    -58.9972808661260f},
  { 75.9637565320735f,    -55.5037627099091f},
  { 90.0f,    -50.1944289077348f},
  { 0.0f,    -60.2551187030578f},
  { 18.4349488229220f,    -65.6887386511478f},
  { 45.0000000000000f,    -67.9982863255502f},
  { 71.5650511770780f,    -65.6887386511478f},
  { 90.0f,    -60.2551187030578f},
  { 0.0f,    -69.4439547804165f},
  { 26.5650511770780f,    -74.3838705949755f},
  { 63.4349488229220f,    -74.3838705949755f},
  { 90.0f,    -69.4439547804165f},
  { 0.0f,    -77.4711922908485f},
  { 45.0f,    -81.0698581640985f},
  { 90.0f,    -77.4711922908485f},
  { 0.0f,    -84.2894068625003f},
  { 90.0f,    -84.2894068625003f},
  { 96.3401917459099f,    -6.30172637399719f},
  { 104.036243467927f,    -6.91437177215212f},
  { 113.198590513648f,    -7.48050889170827f},
  { 123.690067525980f,    -7.89514210504579f},
  { 135.0f,    -8.04946697552840f},
  { 146.309932474020f,    -7.89514210504579f},
  { 156.801409486352f,    -7.48050889170827f},
  { 165.963756532074f,    -6.91437177215212f},
  { 173.659808254090f,    -6.30172637399719f},
  { 180.0f,    -5.71059313749965f},
  { 97.1250163489018f,    -13.9320915492581f},
  { 105.945395900923f,    -15.3613953897309f},
  { 116.565051177078f,    -16.6015495990202f},
  { 128.659808254090f,    -17.3460652926699f},
  { 141.340191745910f,    -17.3460652926699f},
  { 153.434948822922f,    -16.6015495990202f},
  { 164.054604099077f,    -15.3613953897309f},
  { 172.874983651098f,    -13.9320915492581f},
  { 180.0f,    -12.5288077091515f},
  { 98.1301023541560f,    -22.9897677736088f},
  { 108.434948822922f,    -25.3769335251523f},
  { 120.963756532074f,    -27.2256279985640f},
  { 135.0f,    -27.9383527296024f},
  { 149.036243467926f,    -27.2256279985640f},
  { 161.565051177078f,    -25.3769335251523f},
  { 171.869897645844f,    -22.9897677736088f},
  { 180.0f,    -20.5560452195835f},
  { 99.4623222080256f,    -33.3287577974902f},
  { 111.801409486352f,    -36.6042764427057f},
  { 126.869897645844f,    -38.6598082540901f},
  { 143.130102354156f,    -38.6598082540901f},
  { 158.198590513648f,    -36.6042764427057f},
  { 170.537677791974f,    -33.3287577974902f},
  { 180.0f,    -29.7448812969422f},
  { 101.309932474020f,    -44.4382406711498f},
  { 116.565051177078f,    -48.1896851042214f},
  { 135.0f,    -49.6844577892274f},
  { 153.434948822922f,    -48.1896851042214f},
  { 168.690067525980f,    -44.4382406711498f},
  { 180.0f,    -39.8055710922652f},
  { 104.036243467927f,    -55.5037627099091f},
  { 123.690067525980f,    -58.9972808661260f},
  { 146.309932474020f,    -58.9972808661260f},
  { 165.963756532074f,    -55.5037627099091f},
  { 180.0f,    -50.1944289077348f},
  { 108.434948822922f,    -65.6887386511478f},
  { 135.0f,    -67.9982863255502f},
  { 161.565051177078f,    -65.6887386511478f},
  { 180.0f,    -60.2551187030578f},
  { 116.565051177078f,    -74.3838705949755f},
  { 153.434948822922f,    -74.3838705949755f},
  { 180.0f,    -69.4439547804165f},
  { 135.0f,    -81.0698581640985f},
  { 180.0f,    -77.4711922908485f},
  { 180.0f,    -84.2894068625003f},
  { -173.659808254090f,    -6.30172637399719f},
  { -165.963756532074f,    -6.91437177215212f},
  { -156.801409486352f,    -7.48050889170827f},
  { -146.309932474020f,    -7.89514210504579f},
  { -135.0f,    -8.04946697552840f},
  { -123.690067525980f,    -7.89514210504579f},
  { -113.198590513648f,    -7.48050889170827f},
  { -104.036243467927f,    -6.91437177215212f},
  { -96.3401917459099f,    -6.30172637399719f},
  { -90.0000000000000f,    -5.71059313749965f},
  { -172.874983651098f,    -13.9320915492581f},
  { -164.054604099077f,    -15.3613953897309f},
  { -153.434948822922f,    -16.6015495990202f},
  { -141.340191745910f,    -17.3460652926699f},
  { -128.659808254090f,    -17.3460652926699f},
  { -116.565051177078f,    -16.6015495990202f},
  { -105.945395900923f,    -15.3613953897309f},
  { -97.1250163489018f,    -13.9320915492581f},
  { -90.0f,    -12.5288077091515f},
  { -171.869897645844f,    -22.9897677736088f},
  { -161.565051177078f,    -25.3769335251523f},
  { -149.036243467926f,    -27.2256279985640f},
  { -135.0f,    -27.9383527296024f},
  { -120.963756532074f,    -27.2256279985640f},
  { -108.434948822922f,    -25.3769335251523f},
  { -98.1301023541560f,    -22.9897677736088f},
  { -90.0f,    -20.5560452195835f},
  { -170.537677791974f,    -33.3287577974902f},
  { -158.198590513648f,    -36.6042764427057f},
  { -143.130102354156f,    -38.6598082540901f},
  { -126.869897645844f,    -38.6598082540901f},
  { -111.801409486352f,    -36.6042764427057f},
  { -99.4623222080256f,    -33.3287577974902f},
  { -90.0f,    -29.7448812969422f},
  { -168.690067525980f,    -44.4382406711498f},
  { -153.434948822922f,    -48.1896851042214f},
  { -135.0f,    -49.6844577892274f},
  { -116.565051177078f,    -48.1896851042214f},
  { -101.309932474020f,    -44.4382406711498f},
  { -90.0f,    -39.8055710922652f},
  { -165.963756532074f,    -55.5037627099091f},
  { -146.309932474020f,    -58.9972808661260f},
  { -123.690067525980f,    -58.9972808661260f},
  { -104.036243467927f,    -55.5037627099091f},
  { -90.0f,    -50.1944289077348f},
  { -161.565051177078f,    -65.6887386511478f},
  { -135.0f,    -67.9982863255502f},
  { -108.434948822922f,    -65.6887386511478f},
  { -90.0f,    -60.2551187030578f},
  { -153.434948822922f,    -74.3838705949755f},
  { -116.565051177078f,    -74.3838705949755f},
  { -90.0f,    -69.4439547804165f},
  { -135.0f,    -81.0698581640985f},
  { -90.0f,    -77.4711922908485f},
  { -90.0f,    -84.2894068625003f},
  { -83.6598082540901f,    -6.30172637399719f},
  { -75.9637565320735f,    -6.91437177215212f},
  { -66.8014094863518f,    -7.48050889170827f},
  { -56.3099324740202f,    -7.89514210504579f},
  { -45.0000000000000f,    -8.04946697552840f},
  { -33.6900675259798f,    -7.89514210504579f},
  { -23.1985905136482f,    -7.48050889170827f},
  { -14.0362434679265f,    -6.91437177215212f},
  { -6.34019174590991f,    -6.30172637399719f},
  { -82.8749836510982f,    -13.9320915492581f},
  { -74.0546040990772f,    -15.3613953897309f},
  { -63.4349488229220f,    -16.6015495990202f},
  { -51.3401917459099f,    -17.3460652926699f},
  { -38.6598082540901f,    -17.3460652926699f},
  { -26.5650511770780f,    -16.6015495990202f},
  { -15.9453959009229f,    -15.3613953897309f},
  { -7.12501634890180f,    -13.9320915492581f},
  { -81.8698976458440f,    -22.9897677736088f},
  { -71.5650511770780f,    -25.3769335251523f},
  { -59.0362434679265f,    -27.2256279985640f},
  { -45.0000000000000f,    -27.9383527296024f},
  { -30.9637565320735f,    -27.2256279985640f},
  { -18.4349488229220f,    -25.3769335251523f},
  { -8.13010235415598f,    -22.9897677736088f},
  { -80.5376777919744f,    -33.3287577974902f},
  { -68.1985905136482f,    -36.6042764427057f},
  { -53.1301023541560f,    -38.6598082540901f},
  { -36.8698976458440f,    -38.6598082540901f},
  { -21.8014094863518f,    -36.6042764427057f},
  { -9.46232220802561f,    -33.3287577974902f},
  { -78.6900675259798f,    -44.4382406711498f},
  { -63.4349488229220f,    -48.1896851042214f},
  { -45.0f,    -49.6844577892274f},
  { -26.5650511770780f,    -48.1896851042214f},
  { -11.3099324740202f,    -44.4382406711498f},
  { -75.9637565320735f,    -55.5037627099091f},
  { -56.3099324740202f,    -58.9972808661260f},
  { -33.6900675259798f,    -58.9972808661260f},
  { -14.0362434679265f,    -55.5037627099091f},
  { -71.5650511770780f,    -65.6887386511478f},
  { -45.0000000000000f,    -67.9982863255502f},
  { -18.4349488229220f,    -65.6887386511478f},
  { -63.4349488229220f,    -74.3838705949755f},
  { -26.5650511770780f,    -74.3838705949755f},
  { -45.0f,    -81.0698581640985f}};
 
/* 3LD geosphere 'oct' [12 0] (578 points) */
const float __geosphere_oct_12_0_dirs_deg[578][2] =
{ { 0.0f,    0.0f},
  { 180.0f,    0.0f},
  { 90.0f,    0.0f},
  { -90.0f,    0.0f},
  { 0.0f,    90.0f},
  { 0.0f,    -90.0f},
  { 0.0f,    5.19442890773481f},
  { 0.0f,    11.3099324740202f},
  { 0.0f,    18.4349488229220f},
  { 0.0f,    26.5650511770780f},
  { 0.0f,    35.5376777919744f},
  { 0.0f,    45.0f},
  { 0.0f,    54.4623222080256f},
  { 0.0f,    63.4349488229220f},
  { 0.0f,    71.5650511770780f},
  { 0.0f,    78.6900675259798f},
  { 0.0f,    84.8055710922652f},
  { 5.19442890773481f,    0.0f},
  { 5.71059313749964f,    5.68243848351684f},
  { 6.34019174590991f,    12.4545763684750f},
  { 7.12501634890180f,    20.4104455216585f},
  { 8.13010235415598f,    29.4962084965664f},
  { 9.46232220802562f,    39.4200315639073f},
  { 11.3099324740202f,    49.6408995433388f},
  { 14.0362434679265f,    59.5012730133354f},
  { 18.4349488229220f,    68.4318705643521f},
  { 26.5650511770780f,    76.0472636044633f},
  { 45.0000000000000f,    81.9505330244716f},
  { 89.9999999999999f,    84.8055710922652f},
  { 11.3099324740202f,    0.0f},
  { 12.5288077091515f,    6.19039945857186f},
  { 14.0362434679265f,    13.6330222253664f},
  { 15.9453959009229f,    22.3956623300392f},
  { 18.4349488229220f,    32.3115332374239f},
  { 21.8014094863518f,    42.8759886666357f},
  { 26.5650511770780f,    53.3007747995101f},
  { 33.6900675259798f,    62.7479663251258f},
  { 45.0000000000000f,    70.5287793655093f},
  { 63.4349488229220f,    76.0472636044633f},
  { 90.0f,    78.6900675259798f},
  { 18.4349488229220f,    0.0f},
  { 20.5560452195835f,    6.67559216607672f},
  { 23.1985905136482f,    14.7143535884335f},
  { 26.5650511770780f,    24.0948425521107f},
  { 30.9637565320735f,    34.4499019879535f},
  { 36.8698976458440f,    45.0f},
  { 45.0f,    54.7356103172453f},
  { 56.3099324740202f,    62.7479663251258f},
  { 71.5650511770780f,    68.4318705643521f},
  { 90.0f,    71.5650511770780f},
  { 26.5650511770780f,    0.0f},
  { 29.7448812969422f,    7.07055511696583f},
  { 33.6900675259798f,    15.5013595669370f},
  { 38.6598082540901f,    25.1040902502214f},
  { 45.0000000000000f,    35.2643896827547f},
  { 53.1301023541560f,    45.0000000000000f},
  { 63.4349488229220f,    53.3007747995101f},
  { 75.9637565320735f,    59.5012730133354f},
  { 90.0f,    63.4349488229220f},
  { 35.5376777919744f,    0.0f},
  { 39.8055710922652f,    7.29627530101671f},
  { 45.0000000000000f,    15.7931690482640f},
  { 51.3401917459099f,    25.1040902502214f},
  { 59.0362434679265f,    34.4499019879535f},
  { 68.1985905136482f,    42.8759886666357f},
  { 78.6900675259798f,    49.6408995433388f},
  { 90.0f,    54.4623222080256f},
  { 45.0f,    0.0f},
  { 50.1944289077348f,    7.29627530101671f},
  { 56.3099324740202f,    15.5013595669370f},
  { 63.4349488229220f,    24.0948425521107f},
  { 71.5650511770780f,    32.3115332374238f},
  { 80.5376777919744f,    39.4200315639073f},
  { 90.0f,    45.0f},
  { 54.4623222080256f,    0.0f},
  { 60.2551187030578f,    7.07055511696583f},
  { 66.8014094863518f,    14.7143535884335f},
  { 74.0546040990772f,    22.3956623300392f},
  { 81.8698976458440f,    29.4962084965664f},
  { 90.0f,    35.5376777919744f},
  { 63.4349488229220f,    0.0f},
  { 69.4439547804165f,    6.67559216607672f},
  { 75.9637565320735f,    13.6330222253664f},
  { 82.8749836510982f,    20.4104455216585f},
  { 90.0f,    26.5650511770780f},
  { 71.5650511770780f,    0.0f},
  { 77.4711922908485f,    6.19039945857186f},
  { 83.6598082540901f,    12.4545763684750f},
  { 90.0f,    18.4349488229220f},
  { 78.6900675259798f,    0.0f},
  { 84.2894068625004f,    5.68243848351684f},
  { 90.0f,    11.3099324740202f},
  { 84.8055710922652f,    0.0f},
  { 90.0f,    5.19442890773481f},
  { 95.1944289077348f,    0.0f},
  { 95.7105931374996f,    5.68243848351684f},
  { 96.3401917459099f,    12.4545763684750f},
  { 97.1250163489018f,    20.4104455216585f},
  { 98.1301023541560f,    29.4962084965664f},
  { 99.4623222080256f,    39.4200315639073f},
  { 101.309932474020f,    49.6408995433388f},
  { 104.036243467927f,    59.5012730133354f},
  { 108.434948822922f,    68.4318705643521f},
  { 116.565051177078f,    76.0472636044633f},
  { 135.0f,    81.9505330244716f},
  { 180.000000000000f,    84.8055710922652f},
  { 101.309932474020f,    0.0f},
  { 102.528807709152f,    6.19039945857186f},
  { 104.036243467927f,    13.6330222253664f},
  { 105.945395900923f,    22.3956623300392f},
  { 108.434948822922f,    32.3115332374239f},
  { 111.801409486352f,    42.8759886666357f},
  { 116.565051177078f,    53.3007747995101f},
  { 123.690067525980f,    62.7479663251258f},
  { 135.0f,    70.5287793655093f},
  { 153.434948822922f,    76.0472636044633f},
  { 180.0f,    78.6900675259798f},
  { 108.434948822922f,    0.0f},
  { 110.556045219583f,    6.67559216607672f},
  { 113.198590513648f,    14.7143535884335f},
  { 116.565051177078f,    24.0948425521107f},
  { 120.963756532074f,    34.4499019879535f},
  { 126.869897645844f,    45.0f},
  { 135.0f,    54.7356103172453f},
  { 146.309932474020f,    62.7479663251258f},
  { 161.565051177078f,    68.4318705643521f},
  { 180.0f,    71.5650511770780f},
  { 116.565051177078f,    0.0f},
  { 119.744881296942f,    7.07055511696583f},
  { 123.690067525980f,    15.5013595669370f},
  { 128.659808254090f,    25.1040902502214f},
  { 135.0f,    35.2643896827547f},
  { 143.130102354156f,    45.0000000000000f},
  { 153.434948822922f,    53.3007747995101f},
  { 165.963756532074f,    59.5012730133354f},
  { 180.0f,    63.4349488229220f},
  { 125.537677791974f,    0.0f},
  { 129.805571092265f,    7.29627530101671f},
  { 135.0f,    15.7931690482640f},
  { 141.340191745910f,    25.1040902502214f},
  { 149.036243467926f,    34.4499019879535f},
  { 158.198590513648f,    42.8759886666357f},
  { 168.690067525980f,    49.6408995433388f},
  { 180.0f,    54.4623222080256f},
  { 135.0f,    0.0f},
  { 140.194428907735f,    7.29627530101671f},
  { 146.309932474020f,    15.5013595669370f},
  { 153.434948822922f,    24.0948425521107f},
  { 161.565051177078f,    32.3115332374238f},
  { 170.537677791974f,    39.4200315639073f},
  { 180.0f,    45.0f},
  { 144.462322208026f,    0.0f},
  { 150.255118703058f,    7.07055511696583f},
  { 156.801409486352f,    14.7143535884335f},
  { 164.054604099077f,    22.3956623300392f},
  { 171.869897645844f,    29.4962084965664f},
  { 180.0f,    35.5376777919744f},
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  { -101.309932474020f,    -49.6408995433388f},
  { -90.0f,    -45.0f},
  { -165.963756532074f,    -59.5012730133354f},
  { -146.309932474020f,    -62.7479663251258f},
  { -123.690067525980f,    -62.7479663251258f},
  { -104.036243467927f,    -59.5012730133354f},
  { -90.0f,    -54.4623222080256f},
  { -161.565051177078f,    -68.4318705643521f},
  { -135.0f,    -70.5287793655093f},
  { -108.434948822922f,    -68.4318705643521f},
  { -90.0f,    -63.4349488229220f},
  { -153.434948822922f,    -76.0472636044633f},
  { -116.565051177078f,    -76.0472636044633f},
  { -90.0f,    -71.5650511770780f},
  { -135.0f,    -81.9505330244716f},
  { -90.0f,    -78.6900675259798f},
  { -90.0f,    -84.8055710922652f},
  { -84.2894068625004f,    -5.68243848351684f},
  { -77.4711922908485f,    -6.19039945857186f},
  { -69.4439547804165f,    -6.67559216607672f},
  { -60.2551187030578f,    -7.07055511696583f},
  { -50.1944289077348f,    -7.29627530101671f},
  { -39.8055710922652f,    -7.29627530101671f},
  { -29.7448812969422f,    -7.07055511696583f},
  { -20.5560452195835f,    -6.67559216607672f},
  { -12.5288077091515f,    -6.19039945857186f},
  { -5.71059313749965f,    -5.68243848351684f},
  { -83.6598082540901f,    -12.4545763684750f},
  { -75.9637565320735f,    -13.6330222253664f},
  { -66.8014094863518f,    -14.7143535884335f},
  { -56.3099324740202f,    -15.5013595669370f},
  { -45.0f,    -15.7931690482640f},
  { -33.6900675259798f,    -15.5013595669370f},
  { -23.1985905136482f,    -14.7143535884335f},
  { -14.0362434679265f,    -13.6330222253664f},
  { -6.34019174590991f,    -12.4545763684750f},
  { -82.8749836510982f,    -20.4104455216585f},
  { -74.0546040990772f,    -22.3956623300392f},
  { -63.4349488229220f,    -24.0948425521107f},
  { -51.3401917459099f,    -25.1040902502214f},
  { -38.6598082540901f,    -25.1040902502214f},
  { -26.5650511770780f,    -24.0948425521107f},
  { -15.9453959009228f,    -22.3956623300392f},
  { -7.12501634890180f,    -20.4104455216585f},
  { -81.8698976458440f,    -29.4962084965664f},
  { -71.5650511770780f,    -32.3115332374238f},
  { -59.0362434679265f,    -34.4499019879535f},
  { -45.0000000000000f,    -35.2643896827547f},
  { -30.9637565320735f,    -34.4499019879535f},
  { -18.4349488229220f,    -32.3115332374238f},
  { -8.13010235415598f,    -29.4962084965664f},
  { -80.5376777919744f,    -39.4200315639073f},
  { -68.1985905136482f,    -42.8759886666357f},
  { -53.1301023541560f,    -45.0000000000000f},
  { -36.8698976458440f,    -45.0000000000000f},
  { -21.8014094863518f,    -42.8759886666357f},
  { -9.46232220802562f,    -39.4200315639073f},
  { -78.6900675259798f,    -49.6408995433388f},
  { -63.4349488229220f,    -53.3007747995101f},
  { -45.0f,    -54.7356103172453f},
  { -26.5650511770780f,    -53.3007747995101f},
  { -11.3099324740202f,    -49.6408995433388f},
  { -75.9637565320735f,    -59.5012730133354f},
  { -56.3099324740202f,    -62.7479663251258f},
  { -33.6900675259798f,    -62.7479663251258f},
  { -14.0362434679265f,    -59.5012730133354f},
  { -71.5650511770780f,    -68.4318705643521f},
  { -45.0000000000000f,    -70.5287793655093f},
  { -18.4349488229220f,    -68.4318705643521f},
  { -63.4349488229220f,    -76.0472636044633f},
  { -26.5650511770780f,    -76.0472636044633f},
  { -45.0f,    -81.9505330244716f}};
 
/* 3LD geosphere 'oct' [13 0] (678 points) */
const float __geosphere_oct_13_0_dirs_deg[678][2] =
{ { 0.0f,    0.0f},
  { 180.0f,    0.0f},
  { 90.0f,    0.0f},
  { -90.0f,    0.0f},
  { 0.0f,    90.0f},
  { 0.0f,    -90.0f},
  { 0.0f,    4.76364169072618f},
  { 0.0f,    10.3048464687660f},
  { 0.0f,    16.6992442339936f},
  { 0.0f,    23.9624889745782f},
  { 0.0f,    32.0053832080835f},
  { 0.0f,    40.6012946450045f},
  { 0.0f,    49.3987053549955f},
  { 0.0f,    57.9946167919165f},
  { 0.0f,    66.0375110254218f},
  { 0.0f,    73.3007557660064f},
  { 0.0f,    79.6951535312340f},
  { 0.0f,    85.2363583092738f},
  { 4.76364169072618f,    0.0f},
  { 5.19442890773481f,    5.17321244611695f},
  { 5.71059313749964f,    11.2552397326621f},
  { 6.34019174590991f,    18.3297537440740f},
  { 7.12501634890180f,    26.3877999612430f},
  { 8.13010235415598f,    35.2643896827547f},
  { 9.46232220802562f,    44.6075508793597f},
  { 11.3099324740202f,    53.9292313492037f},
  { 14.0362434679265f,    62.7339555492672f},
  { 18.4349488229220f,    70.6403513388797f},
  { 26.5650511770780f,    77.3956173516208f},
  { 45.0000000000000f,    82.6739630468477f},
  { 89.9999999999999f,    85.2363583092738f},
  { 10.3048464687660f,    0.0f},
  { 11.3099324740202f,    5.60040918481662f},
  { 12.5288077091515f,    12.2395582977766f},
  { 14.0362434679265f,    19.9915607271414f},
  { 15.9453959009229f,    28.7862533091452f},
  { 18.4349488229220f,    38.3288181014559f},
  { 21.8014094863518f,    48.0911521181967f},
  { 26.5650511770780f,    57.4264443008031f},
  { 33.6900675259798f,    65.7392004151320f},
  { 45.0f,    72.5536476627867f},
  { 63.4349488229220f,    77.3956173516208f},
  { 90.0000000000001f,    79.6951535312340f},
  { 16.6992442339936f,    0.0f},
  { 18.4349488229220f,    6.01728486403203f},
  { 20.5560452195835f,    13.1747121595676f},
  { 23.1985905136482f,    21.5004376144442f},
  { 26.5650511770780f,    30.8069811171052f},
  { 30.9637565320735f,    40.6128551760767f},
  { 36.8698976458440f,    50.1944289077348f},
  { 45.0000000000000f,    58.7803015526316f},
  { 56.3099324740202f,    65.7392004151319f},
  { 71.5650511770780f,    70.6403513388797f},
  { 90.0f,    73.3007557660064f},
  { 23.9624889745782f,    0.0f},
  { 26.5650511770780f,    6.37937020844280f},
  { 29.7448812969422f,    13.9320915492581f},
  { 33.6900675259798f,    22.5885387879849f},
  { 38.6598082540901f,    31.9928170001817f},
  { 45.0f,    41.4729343089405f},
  { 53.1301023541560f,    50.1944289077348f},
  { 63.4349488229220f,    57.4264443008031f},
  { 75.9637565320735f,    62.7339555492672f},
  { 90.0f,    66.0375110254218f},
  { 32.0053832080835f,    0.0f},
  { 35.5376777919744f,    6.63073776807866f},
  { 39.8055710922652f,    14.3633026740704f},
  { 45.0000000000000f,    22.9897677736089f},
  { 51.3401917459099f,    31.9928170001817f},
  { 59.0362434679265f,    40.6128551760767f},
  { 68.1985905136482f,    48.0911521181967f},
  { 78.6900675259798f,    53.9292313492037f},
  { 90.0f,    57.9946167919165f},
  { 40.6012946450045f,    0.0f},
  { 45.0000000000000f,    6.72136933936946f},
  { 50.1944289077348f,    14.3633026740704f},
  { 56.3099324740202f,    22.5885387879849f},
  { 63.4349488229220f,    30.8069811171052f},
  { 71.5650511770780f,    38.3288181014559f},
  { 80.5376777919744f,    44.6075508793597f},
  { 90.0f,    49.3987053549955f},
  { 49.3987053549955f,    0.0f},
  { 54.4623222080256f,    6.63073776807866f},
  { 60.2551187030578f,    13.9320915492581f},
  { 66.8014094863518f,    21.5004376144442f},
  { 74.0546040990771f,    28.7862533091452f},
  { 81.8698976458440f,    35.2643896827547f},
  { 90.0f,    40.6012946450045f},
  { 57.9946167919165f,    0.0f},
  { 63.4349488229220f,    6.37937020844280f},
  { 69.4439547804165f,    13.1747121595676f},
  { 75.9637565320735f,    19.9915607271414f},
  { 82.8749836510982f,    26.3877999612430f},
  { 90.0f,    32.0053832080835f},
  { 66.0375110254218f,    0.0f},
  { 71.5650511770780f,    6.01728486403203f},
  { 77.4711922908485f,    12.2395582977766f},
  { 83.6598082540901f,    18.3297537440740f},
  { 90.0f,    23.9624889745782f},
  { 73.3007557660064f,    0.0f},
  { 78.6900675259798f,    5.60040918481662f},
  { 84.2894068625004f,    11.2552397326621f},
  { 90.0f,    16.6992442339936f},
  { 79.6951535312340f,    0.0f},
  { 84.8055710922652f,    5.17321244611695f},
  { 90.0f,    10.3048464687660f},
  { 85.2363583092738f,    0.0f},
  { 90.0f,    4.76364169072617f},
  { 94.7636416907262f,    0.0f},
  { 95.1944289077348f,    5.17321244611695f},
  { 95.7105931374996f,    11.2552397326621f},
  { 96.3401917459099f,    18.3297537440740f},
  { 97.1250163489018f,    26.3877999612430f},
  { 98.1301023541560f,    35.2643896827547f},
  { 99.4623222080256f,    44.6075508793597f},
  { 101.309932474020f,    53.9292313492037f},
  { 104.036243467927f,    62.7339555492672f},
  { 108.434948822922f,    70.6403513388797f},
  { 116.565051177078f,    77.3956173516208f},
  { 135.000000000000f,    82.6739630468477f},
  { 180.000000000000f,    85.2363583092738f},
  { 100.304846468766f,    0.0f},
  { 101.309932474020f,    5.60040918481662f},
  { 102.528807709152f,    12.2395582977766f},
  { 104.036243467927f,    19.9915607271414f},
  { 105.945395900923f,    28.7862533091452f},
  { 108.434948822922f,    38.3288181014559f},
  { 111.801409486352f,    48.0911521181967f},
  { 116.565051177078f,    57.4264443008031f},
  { 123.690067525980f,    65.7392004151319f},
  { 135.0f,    72.5536476627867f},
  { 153.434948822922f,    77.3956173516208f},
  { -180.000000000000f,    79.6951535312340f},
  { 106.699244233994f,    0.0f},
  { 108.434948822922f,    6.01728486403203f},
  { 110.556045219583f,    13.1747121595676f},
  { 113.198590513648f,    21.5004376144442f},
  { 116.565051177078f,    30.8069811171052f},
  { 120.963756532074f,    40.6128551760767f},
  { 126.869897645844f,    50.1944289077348f},
  { 135.0f,    58.7803015526316f},
  { 146.309932474020f,    65.7392004151319f},
  { 161.565051177078f,    70.6403513388797f},
  { 180.0f,    73.3007557660064f},
  { 113.962488974578f,    0.0f},
  { 116.565051177078f,    6.37937020844280f},
  { 119.744881296942f,    13.9320915492581f},
  { 123.690067525980f,    22.5885387879849f},
  { 128.659808254090f,    31.9928170001817f},
  { 135.0f,    41.4729343089405f},
  { 143.130102354156f,    50.1944289077348f},
  { 153.434948822922f,    57.4264443008031f},
  { 165.963756532074f,    62.7339555492672f},
  { 180.0f,    66.0375110254218f},
  { 122.005383208084f,    0.0f},
  { 125.537677791974f,    6.63073776807866f},
  { 129.805571092265f,    14.3633026740704f},
  { 135.0f,    22.9897677736089f},
  { 141.340191745910f,    31.9928170001817f},
  { 149.036243467926f,    40.6128551760767f},
  { 158.198590513648f,    48.0911521181967f},
  { 168.690067525980f,    53.9292313492037f},
  { 180.0f,    57.9946167919165f},
  { 130.601294645005f,    0.0f},
  { 135.0f,    6.72136933936946f},
  { 140.194428907735f,    14.3633026740704f},
  { 146.309932474020f,    22.5885387879849f},
  { 153.434948822922f,    30.8069811171052f},
  { 161.565051177078f,    38.3288181014559f},
  { 170.537677791974f,    44.6075508793597f},
  { 180.0f,    49.3987053549955f},
  { 139.398705354996f,    0.0f},
  { 144.462322208026f,    6.63073776807866f},
  { 150.255118703058f,    13.9320915492581f},
  { 156.801409486352f,    21.5004376144442f},
  { 164.054604099077f,    28.7862533091452f},
  { 171.869897645844f,    35.2643896827547f},
  { 180.0f,    40.6012946450045f},
  { 147.994616791917f,    0.0f},
  { 153.434948822922f,    6.37937020844280f},
  { 159.443954780417f,    13.1747121595676f},
  { 165.963756532074f,    19.9915607271414f},
  { 172.874983651098f,    26.3877999612430f},
  { 180.0f,    32.0053832080835f},
  { 156.037511025422f,    0.0f},
  { 161.565051177078f,    6.01728486403203f},
  { 167.471192290848f,    12.2395582977766f},
  { 173.659808254090f,    18.3297537440740f},
  { 180.0f,    23.9624889745782f},
  { 163.300755766006f,    0.0f},
  { 168.690067525980f,    5.60040918481661f},
  { 174.289406862500f,    11.2552397326621f},
  { 180.0f,    16.6992442339936f},
  { 169.695153531234f,    0.0f},
  { 174.805571092265f,    5.17321244611695f},
  { 180.0f,    10.3048464687660f},
  { 175.236358309274f,    0.0f},
  { 180.0f,    4.76364169072617f},
  { -175.236358309274f,    0.0f},
  { -174.805571092265f,    5.17321244611695f},
  { -174.289406862500f,    11.2552397326621f},
  { -173.659808254090f,    18.3297537440740f},
  { -172.874983651098f,    26.3877999612430f},
  { -171.869897645844f,    35.2643896827547f},
  { -170.537677791974f,    44.6075508793597f},
  { -168.690067525980f,    53.9292313492036f},
  { -165.963756532074f,    62.7339555492672f},
  { -161.565051177078f,    70.6403513388797f},
  { -153.434948822922f,    77.3956173516208f},
  { -135.0f,    82.6739630468477f},
  { -90.0000000000001f,    85.2363583092738f},
  { -169.695153531234f,    0.0f},
  { -168.690067525980f,    5.60040918481662f},
  { -167.471192290848f,    12.2395582977766f},
  { -165.963756532074f,    19.9915607271414f},
  { -164.054604099077f,    28.7862533091452f},
  { -161.565051177078f,    38.3288181014559f},
  { -158.198590513648f,    48.0911521181967f},
  { -153.434948822922f,    57.4264443008031f},
  { -146.309932474020f,    65.7392004151320f},
  { -135.0f,    72.5536476627867f},
  { -116.565051177078f,    77.3956173516208f},
  { -90.0000000000000f,    79.6951535312340f},
  { -163.300755766006f,    0.0f},
  { -161.565051177078f,    6.01728486403203f},
  { -159.443954780417f,    13.1747121595676f},
  { -156.801409486352f,    21.5004376144442f},
  { -153.434948822922f,    30.8069811171052f},
  { -149.036243467926f,    40.6128551760767f},
  { -143.130102354156f,    50.1944289077348f},
  { -135.0f,    58.7803015526316f},
  { -123.690067525980f,    65.7392004151319f},
  { -108.434948822922f,    70.6403513388797f},
  { -90.0f,    73.3007557660064f},
  { -156.037511025422f,    0.0f},
  { -153.434948822922f,    6.37937020844280f},
  { -150.255118703058f,    13.9320915492581f},
  { -146.309932474020f,    22.5885387879849f},
  { -141.340191745910f,    31.9928170001817f},
  { -135.0f,    41.4729343089405f},
  { -126.869897645844f,    50.1944289077348f},
  { -116.565051177078f,    57.4264443008031f},
  { -104.036243467927f,    62.7339555492672f},
  { -90.0f,    66.0375110254218f},
  { -147.994616791916f,    0.0f},
  { -144.462322208026f,    6.63073776807866f},
  { -140.194428907735f,    14.3633026740704f},
  { -135.0f,    22.9897677736089f},
  { -128.659808254090f,    31.9928170001817f},
  { -120.963756532074f,    40.6128551760767f},
  { -111.801409486352f,    48.0911521181967f},
  { -101.309932474020f,    53.9292313492037f},
  { -90.0f,    57.9946167919165f},
  { -139.398705354996f,    0.0f},
  { -135.0f,    6.72136933936946f},
  { -129.805571092265f,    14.3633026740704f},
  { -123.690067525980f,    22.5885387879849f},
  { -116.565051177078f,    30.8069811171052f},
  { -108.434948822922f,    38.3288181014559f},
  { -99.4623222080256f,    44.6075508793597f},
  { -90.0f,    49.3987053549955f},
  { -130.601294645005f,    0.0f},
  { -125.537677791974f,    6.63073776807866f},
  { -119.744881296942f,    13.9320915492581f},
  { -113.198590513648f,    21.5004376144442f},
  { -105.945395900923f,    28.7862533091452f},
  { -98.1301023541560f,    35.2643896827547f},
  { -90.0000000000000f,    40.6012946450045f},
  { -122.005383208084f,    0.0f},
  { -116.565051177078f,    6.37937020844280f},
  { -110.556045219583f,    13.1747121595676f},
  { -104.036243467927f,    19.9915607271414f},
  { -97.1250163489018f,    26.3877999612430f},
  { -90.0f,    32.0053832080835f},
  { -113.962488974578f,    0.0f},
  { -108.434948822922f,    6.01728486403203f},
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  { -63.4349488229220f,    -6.37937020844280f},
  { -54.4623222080256f,    -6.63073776807866f},
  { -45.0000000000000f,    -6.72136933936946f},
  { -35.5376777919744f,    -6.63073776807866f},
  { -26.5650511770780f,    -6.37937020844280f},
  { -18.4349488229220f,    -6.01728486403203f},
  { -11.3099324740202f,    -5.60040918481662f},
  { -5.19442890773480f,    -5.17321244611695f},
  { -84.2894068625003f,    -11.2552397326621f},
  { -77.4711922908485f,    -12.2395582977766f},
  { -69.4439547804165f,    -13.1747121595676f},
  { -60.2551187030578f,    -13.9320915492581f},
  { -50.1944289077348f,    -14.3633026740704f},
  { -39.8055710922652f,    -14.3633026740704f},
  { -29.7448812969422f,    -13.9320915492581f},
  { -20.5560452195835f,    -13.1747121595676f},
  { -12.5288077091515f,    -12.2395582977766f},
  { -5.71059313749964f,    -11.2552397326621f},
  { -83.6598082540901f,    -18.3297537440740f},
  { -75.9637565320735f,    -19.9915607271414f},
  { -66.8014094863518f,    -21.5004376144442f},
  { -56.3099324740202f,    -22.5885387879849f},
  { -45.0000000000000f,    -22.9897677736089f},
  { -33.6900675259798f,    -22.5885387879849f},
  { -23.1985905136482f,    -21.5004376144442f},
  { -14.0362434679265f,    -19.9915607271414f},
  { -6.34019174590991f,    -18.3297537440740f},
  { -82.8749836510982f,    -26.3877999612430f},
  { -74.0546040990771f,    -28.7862533091452f},
  { -63.4349488229220f,    -30.8069811171052f},
  { -51.3401917459099f,    -31.9928170001817f},
  { -38.6598082540901f,    -31.9928170001817f},
  { -26.5650511770780f,    -30.8069811171052f},
  { -15.9453959009229f,    -28.7862533091452f},
  { -7.12501634890179f,    -26.3877999612430f},
  { -81.8698976458440f,    -35.2643896827547f},
  { -71.5650511770780f,    -38.3288181014559f},
  { -59.0362434679265f,    -40.6128551760767f},
  { -45.0f,    -41.4729343089405f},
  { -30.9637565320735f,    -40.6128551760767f},
  { -18.4349488229220f,    -38.3288181014559f},
  { -8.13010235415597f,    -35.2643896827547f},
  { -80.5376777919744f,    -44.6075508793597f},
  { -68.1985905136482f,    -48.0911521181967f},
  { -53.1301023541560f,    -50.1944289077348f},
  { -36.8698976458440f,    -50.1944289077348f},
  { -21.8014094863518f,    -48.0911521181967f},
  { -9.46232220802561f,    -44.6075508793597f},
  { -78.6900675259798f,    -53.9292313492037f},
  { -63.4349488229220f,    -57.4264443008031f},
  { -45.0000000000000f,    -58.7803015526316f},
  { -26.5650511770780f,    -57.4264443008031f},
  { -11.3099324740202f,    -53.9292313492037f},
  { -75.9637565320735f,    -62.7339555492672f},
  { -56.3099324740202f,    -65.7392004151320f},
  { -33.6900675259798f,    -65.7392004151320f},
  { -14.0362434679265f,    -62.7339555492672f},
  { -71.5650511770780f,    -70.6403513388797f},
  { -45.0f,    -72.5536476627867f},
  { -18.4349488229220f,    -70.6403513388797f},
  { -63.4349488229220f,    -77.3956173516208f},
  { -26.5650511770780f,    -77.3956173516208f},
  { -45.0f,    -82.6739630468477f}};
 
/* 3LD geosphere 'oct' [14 0] (786 points) */
const float __geosphere_oct_14_0_dirs_deg[786][2] =
{ { 0.0f,    0.0f},
  { 180.0f,    0.0f},
  { 90.0f,    0.0f},
  { -90.0f,    0.0f},
  { 0.0f,    90.0f},
  { 0.0f,    -90.0f},
  { 0.0f,    4.39870535499553f},
  { 0.0f,    9.46232220802562f},
  { 0.0f,    15.2551187030578f},
  { 0.0f,    21.8014094863518f},
  { 0.0f,    29.0546040990771f},
  { 0.0f,    36.8698976458440f},
  { 0.0f,    45.0f},
  { 0.0f,    53.1301023541560f},
  { 0.0f,    60.9453959009229f},
  { 0.0f,    68.1985905136482f},
  { 0.0f,    74.7448812969422f},
  { 0.0f,    80.5376777919744f},
  { 0.0f,    85.6012946450045f},
  { 4.39870535499553f,    0.0f},
  { 4.76364169072618f,    4.74726225485260f},
  { 5.19442890773481f,    10.2634278919935f},
  { 5.71059313749964f,    16.6209512676335f},
  { 6.34019174590991f,    23.8322990618998f},
  { 7.12501634890180f,    31.8061000193785f},
  { 8.13010235415598f,    40.3155422107726f},
  { 9.46232220802562f,    49.0104664376223f},
  { 11.3099324740202f,    57.4874826838300f},
  { 14.0362434679265f,    65.3864023470214f},
  { 18.4349488229220f,    72.4515993862077f},
  { 26.5650511770780f,    78.5095400962685f},
  { 45.0000000000000f,    83.2786306606305f},
  { 90.0f,    85.6012946450045f},
  { 9.46232220802562f,    0.0f},
  { 10.3048464687660f,    5.11108969528872f},
  { 11.3099324740202f,    11.0958032831364f},
  { 12.5288077091515f,    18.0246645268103f},
  { 14.0362434679265f,    25.8766900608275f},
  { 15.9453959009229f,    34.4813893719816f},
  { 18.4349488229220f,    43.4915193450920f},
  { 21.8014094863518f,    52.4285827724619f},
  { 26.5650511770780f,    60.7940677526006f},
  { 33.6900675259798f,    68.1681310319003f},
  { 45.0000000000000f,    74.2068309517361f},
  { 63.4349488229220f,    78.5095400962685f},
  { 90.0f,    80.5376777919744f},
  { 15.2551187030578f,    0.0f},
  { 16.6992442339936f,    5.47124945343343f},
  { 18.4349488229220f,    11.9046881128481f},
  { 20.5560452195835f,    19.3473699609355f},
  { 23.1985905136482f,    27.7096107852625f},
  { 26.5650511770780f,    36.6992252004899f},
  { 30.9637565320735f,    45.8186225388889f},
  { 36.8698976458440f,    54.4623222080256f},
  { 45.0000000000000f,    62.0616472703976f},
  { 56.3099324740202f,    68.1681310319003f},
  { 71.5650511770780f,    72.4515993862077f},
  { 90.0f,    74.7448812969422f},
  { 21.8014094863518f,    0.0f},
  { 23.9624889745782f,    5.79763632953063f},
  { 26.5650511770780f,    12.6043826483792f},
  { 29.7448812969422f,    20.4104455216585f},
  { 33.6900675259798f,    29.0171406246015f},
  { 38.6598082540901f,    37.9851672993556f},
  { 45.0000000000000f,    46.6861433417170f},
  { 53.1301023541560f,    54.4623222080256f},
  { 63.4349488229220f,    60.7940677526006f},
  { 75.9637565320735f,    65.3864023470214f},
  { 90.0f,    68.1985905136482f},
  { 29.0546040990771f,    0.0f},
  { 32.0053832080835f,    6.05074601591175f},
  { 35.5376777919744f,    13.0884760858333f},
  { 39.8055710922652f,    21.0123137896886f},
  { 45.0000000000000f,    29.4962084965664f},
  { 51.3401917459099f,    37.9851672993556f},
  { 59.0362434679265f,    45.8186225388889f},
  { 68.1985905136482f,    52.4285827724619f},
  { 78.6900675259798f,    57.4874826838300f},
  { 90.0f,    60.9453959009229f},
  { 36.8698976458440f,    0.0f},
  { 40.6012946450045f,    6.19039945857186f},
  { 45.0f,    13.2626760083048f},
  { 50.1944289077348f,    21.0123137896886f},
  { 56.3099324740202f,    29.0171406246015f},
  { 63.4349488229220f,    36.6992252004899f},
  { 71.5650511770780f,    43.4915193450920f},
  { 80.5376777919744f,    49.0104664376223f},
  { 90.0f,    53.1301023541560f},
  { 45.0f,    0.0f},
  { 49.3987053549955f,    6.19039945857186f},
  { 54.4623222080256f,    13.0884760858333f},
  { 60.2551187030578f,    20.4104455216585f},
  { 66.8014094863518f,    27.7096107852625f},
  { 74.0546040990772f,    34.4813893719816f},
  { 81.8698976458440f,    40.3155422107726f},
  { 90.0f,    45.0f},
  { 53.1301023541560f,    0.0f},
  { 57.9946167919165f,    6.05074601591175f},
  { 63.4349488229220f,    12.6043826483792f},
  { 69.4439547804165f,    19.3473699609355f},
  { 75.9637565320735f,    25.8766900608275f},
  { 82.8749836510982f,    31.8061000193785f},
  { 90.0f,    36.8698976458440f},
  { 60.9453959009229f,    0.0f},
  { 66.0375110254218f,    5.79763632953063f},
  { 71.5650511770780f,    11.9046881128481f},
  { 77.4711922908485f,    18.0246645268103f},
  { 83.6598082540901f,    23.8322990618998f},
  { 90.0f,    29.0546040990771f},
  { 68.1985905136482f,    0.0f},
  { 73.3007557660064f,    5.47124945343343f},
  { 78.6900675259798f,    11.0958032831364f},
  { 84.2894068625004f,    16.6209512676335f},
  { 90.0f,    21.8014094863518f},
  { 74.7448812969422f,    0.0f},
  { 79.6951535312340f,    5.11108969528872f},
  { 84.8055710922652f,    10.2634278919936f},
  { 90.0f,    15.2551187030578f},
  { 80.5376777919744f,    0.0f},
  { 85.2363583092738f,    4.74726225485260f},
  { 90.0f,    9.46232220802562f},
  { 85.6012946450045f,    0.0f},
  { 90.0f,    4.39870535499553f},
  { 94.3987053549955f,    0.0f},
  { 94.7636416907262f,    4.74726225485260f},
  { 95.1944289077348f,    10.2634278919935f},
  { 95.7105931374996f,    16.6209512676335f},
  { 96.3401917459099f,    23.8322990618998f},
  { 97.1250163489018f,    31.8061000193785f},
  { 98.1301023541560f,    40.3155422107726f},
  { 99.4623222080256f,    49.0104664376223f},
  { 101.309932474020f,    57.4874826838300f},
  { 104.036243467927f,    65.3864023470214f},
  { 108.434948822922f,    72.4515993862077f},
  { 116.565051177078f,    78.5095400962685f},
  { 135.000000000000f,    83.2786306606305f},
  { 180.0f,    85.6012946450045f},
  { 99.4623222080256f,    0.0f},
  { 100.304846468766f,    5.11108969528872f},
  { 101.309932474020f,    11.0958032831364f},
  { 102.528807709152f,    18.0246645268103f},
  { 104.036243467927f,    25.8766900608275f},
  { 105.945395900923f,    34.4813893719816f},
  { 108.434948822922f,    43.4915193450920f},
  { 111.801409486352f,    52.4285827724619f},
  { 116.565051177078f,    60.7940677526006f},
  { 123.690067525980f,    68.1681310319003f},
  { 135.000000000000f,    74.2068309517361f},
  { 153.434948822922f,    78.5095400962685f},
  { 180.0f,    80.5376777919744f},
  { 105.255118703058f,    0.0f},
  { 106.699244233994f,    5.47124945343343f},
  { 108.434948822922f,    11.9046881128481f},
  { 110.556045219583f,    19.3473699609355f},
  { 113.198590513648f,    27.7096107852625f},
  { 116.565051177078f,    36.6992252004899f},
  { 120.963756532074f,    45.8186225388889f},
  { 126.869897645844f,    54.4623222080256f},
  { 135.0f,    62.0616472703976f},
  { 146.309932474020f,    68.1681310319003f},
  { 161.565051177078f,    72.4515993862077f},
  { 180.0f,    74.7448812969422f},
  { 111.801409486352f,    0.0f},
  { 113.962488974578f,    5.79763632953063f},
  { 116.565051177078f,    12.6043826483792f},
  { 119.744881296942f,    20.4104455216585f},
  { 123.690067525980f,    29.0171406246015f},
  { 128.659808254090f,    37.9851672993556f},
  { 135.0f,    46.6861433417170f},
  { 143.130102354156f,    54.4623222080256f},
  { 153.434948822922f,    60.7940677526006f},
  { 165.963756532074f,    65.3864023470214f},
  { 180.0f,    68.1985905136482f},
  { 119.054604099077f,    0.0f},
  { 122.005383208084f,    6.05074601591175f},
  { 125.537677791974f,    13.0884760858333f},
  { 129.805571092265f,    21.0123137896886f},
  { 135.0f,    29.4962084965664f},
  { 141.340191745910f,    37.9851672993556f},
  { 149.036243467926f,    45.8186225388889f},
  { 158.198590513648f,    52.4285827724619f},
  { 168.690067525980f,    57.4874826838300f},
  { 180.0f,    60.9453959009229f},
  { 126.869897645844f,    0.0f},
  { 130.601294645005f,    6.19039945857186f},
  { 135.0f,    13.2626760083048f},
  { 140.194428907735f,    21.0123137896886f},
  { 146.309932474020f,    29.0171406246015f},
  { 153.434948822922f,    36.6992252004899f},
  { 161.565051177078f,    43.4915193450920f},
  { 170.537677791974f,    49.0104664376223f},
  { 180.0f,    53.1301023541560f},
  { 135.0f,    0.0f},
  { 139.398705354996f,    6.19039945857186f},
  { 144.462322208026f,    13.0884760858333f},
  { 150.255118703058f,    20.4104455216585f},
  { 156.801409486352f,    27.7096107852625f},
  { 164.054604099077f,    34.4813893719816f},
  { 171.869897645844f,    40.3155422107726f},
  { 180.0f,    45.0f},
  { 143.130102354156f,    0.0f},
  { 147.994616791916f,    6.05074601591175f},
  { 153.434948822922f,    12.6043826483792f},
  { 159.443954780417f,    19.3473699609355f},
  { 165.963756532074f,    25.8766900608275f},
  { 172.874983651098f,    31.8061000193785f},
  { 180.0f,    36.8698976458440f},
  { 150.945395900923f,    0.0f},
  { 156.037511025422f,    5.79763632953063f},
  { 161.565051177078f,    11.9046881128481f},
  { 167.471192290848f,    18.0246645268103f},
  { 173.659808254090f,    23.8322990618998f},
  { 180.0f,    29.0546040990771f},
  { 158.198590513648f,    0.0f},
  { 163.300755766006f,    5.47124945343343f},
  { 168.690067525980f,    11.0958032831364f},
  { 174.289406862500f,    16.6209512676335f},
  { 180.0f,    21.8014094863518f},
  { 164.744881296942f,    0.0f},
  { 169.695153531234f,    5.11108969528872f},
  { 174.805571092265f,    10.2634278919936f},
  { 180.0f,    15.2551187030578f},
  { 170.537677791974f,    0.0f},
  { 175.236358309274f,    4.74726225485260f},
  { 180.0f,    9.46232220802562f},
  { 175.601294645005f,    0.0f},
  { 180.0f,    4.39870535499553f},
  { -175.601294645005f,    0.0f},
  { -175.236358309274f,    4.74726225485260f},
  { -174.805571092265f,    10.2634278919935f},
  { -174.289406862500f,    16.6209512676335f},
  { -173.659808254090f,    23.8322990618998f},
  { -172.874983651098f,    31.8061000193785f},
  { -171.869897645844f,    40.3155422107726f},
  { -170.537677791974f,    49.0104664376223f},
  { -168.690067525980f,    57.4874826838300f},
  { -165.963756532074f,    65.3864023470214f},
  { -161.565051177078f,    72.4515993862077f},
  { -153.434948822922f,    78.5095400962685f},
  { -135.000000000000f,    83.2786306606305f},
  { -90.0f,    85.6012946450045f},
  { -170.537677791974f,    0.0f},
  { -169.695153531234f,    5.11108969528872f},
  { -168.690067525980f,    11.0958032831364f},
  { -167.471192290848f,    18.0246645268103f},
  { -165.963756532074f,    25.8766900608275f},
  { -164.054604099077f,    34.4813893719816f},
  { -161.565051177078f,    43.4915193450920f},
  { -158.198590513648f,    52.4285827724619f},
  { -153.434948822922f,    60.7940677526006f},
  { -146.309932474020f,    68.1681310319003f},
  { -135.0f,    74.2068309517361f},
  { -116.565051177078f,    78.5095400962685f},
  { -90.0f,    80.5376777919744f},
  { -164.744881296942f,    0.0f},
  { -163.300755766006f,    5.47124945343343f},
  { -161.565051177078f,    11.9046881128481f},
  { -159.443954780417f,    19.3473699609355f},
  { -156.801409486352f,    27.7096107852625f},
  { -153.434948822922f,    36.6992252004899f},
  { -149.036243467926f,    45.8186225388889f},
  { -143.130102354156f,    54.4623222080256f},
  { -135.0f,    62.0616472703976f},
  { -123.690067525980f,    68.1681310319003f},
  { -108.434948822922f,    72.4515993862077f},
  { -90.0f,    74.7448812969422f},
  { -158.198590513648f,    0.0f},
  { -156.037511025422f,    5.79763632953063f},
  { -153.434948822922f,    12.6043826483792f},
  { -150.255118703058f,    20.4104455216585f},
  { -146.309932474020f,    29.0171406246015f},
  { -141.340191745910f,    37.9851672993556f},
  { -135.0f,    46.6861433417170f},
  { -126.869897645844f,    54.4623222080256f},
  { -116.565051177078f,    60.7940677526006f},
  { -104.036243467927f,    65.3864023470214f},
  { -90.0f,    68.1985905136482f},
  { -150.945395900923f,    0.0f},
  { -147.994616791916f,    6.05074601591175f},
  { -144.462322208026f,    13.0884760858333f},
  { -140.194428907735f,    21.0123137896886f},
  { -135.0f,    29.4962084965664f},
  { -128.659808254090f,    37.9851672993556f},
  { -120.963756532074f,    45.8186225388889f},
  { -111.801409486352f,    52.4285827724619f},
  { -101.309932474020f,    57.4874826838300f},
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  { -174.805571092265f,    -10.2634278919935f},
  { -168.690067525980f,    -11.0958032831364f},
  { -161.565051177078f,    -11.9046881128481f},
  { -153.434948822922f,    -12.6043826483792f},
  { -144.462322208026f,    -13.0884760858333f},
  { -135.0f,    -13.2626760083048f},
  { -125.537677791974f,    -13.0884760858333f},
  { -116.565051177078f,    -12.6043826483792f},
  { -108.434948822922f,    -11.9046881128481f},
  { -101.309932474020f,    -11.0958032831364f},
  { -95.1944289077348f,    -10.2634278919936f},
  { -90.0f,    -9.46232220802562f},
  { -174.289406862500f,    -16.6209512676335f},
  { -167.471192290848f,    -18.0246645268103f},
  { -159.443954780417f,    -19.3473699609355f},
  { -150.255118703058f,    -20.4104455216585f},
  { -140.194428907735f,    -21.0123137896886f},
  { -129.805571092265f,    -21.0123137896886f},
  { -119.744881296942f,    -20.4104455216585f},
  { -110.556045219583f,    -19.3473699609355f},
  { -102.528807709152f,    -18.0246645268103f},
  { -95.7105931374996f,    -16.6209512676335f},
  { -90.0f,    -15.2551187030578f},
  { -173.659808254090f,    -23.8322990618998f},
  { -165.963756532074f,    -25.8766900608275f},
  { -156.801409486352f,    -27.7096107852625f},
  { -146.309932474020f,    -29.0171406246015f},
  { -135.0f,    -29.4962084965664f},
  { -123.690067525980f,    -29.0171406246015f},
  { -113.198590513648f,    -27.7096107852625f},
  { -104.036243467927f,    -25.8766900608275f},
  { -96.3401917459099f,    -23.8322990618998f},
  { -90.0f,    -21.8014094863518f},
  { -172.874983651098f,    -31.8061000193785f},
  { -164.054604099077f,    -34.4813893719816f},
  { -153.434948822922f,    -36.6992252004899f},
  { -141.340191745910f,    -37.9851672993556f},
  { -128.659808254090f,    -37.9851672993556f},
  { -116.565051177078f,    -36.6992252004899f},
  { -105.945395900923f,    -34.4813893719816f},
  { -97.1250163489018f,    -31.8061000193785f},
  { -90.0f,    -29.0546040990771f},
  { -171.869897645844f,    -40.3155422107726f},
  { -161.565051177078f,    -43.4915193450920f},
  { -149.036243467926f,    -45.8186225388889f},
  { -135.0f,    -46.6861433417170f},
  { -120.963756532074f,    -45.8186225388889f},
  { -108.434948822922f,    -43.4915193450920f},
  { -98.1301023541560f,    -40.3155422107726f},
  { -90.0f,    -36.8698976458440f},
  { -170.537677791974f,    -49.0104664376223f},
  { -158.198590513648f,    -52.4285827724619f},
  { -143.130102354156f,    -54.4623222080256f},
  { -126.869897645844f,    -54.4623222080256f},
  { -111.801409486352f,    -52.4285827724619f},
  { -99.4623222080256f,    -49.0104664376223f},
  { -90.0f,    -45.0f},
  { -168.690067525980f,    -57.4874826838300f},
  { -153.434948822922f,    -60.7940677526006f},
  { -135.0f,    -62.0616472703976f},
  { -116.565051177078f,    -60.7940677526006f},
  { -101.309932474020f,    -57.4874826838300f},
  { -90.0f,    -53.1301023541560f},
  { -165.963756532074f,    -65.3864023470214f},
  { -146.309932474020f,    -68.1681310319003f},
  { -123.690067525980f,    -68.1681310319003f},
  { -104.036243467927f,    -65.3864023470214f},
  { -90.0f,    -60.9453959009229f},
  { -161.565051177078f,    -72.4515993862077f},
  { -135.0f,    -74.2068309517360f},
  { -108.434948822922f,    -72.4515993862077f},
  { -90.0f,    -68.1985905136482f},
  { -153.434948822922f,    -78.5095400962685f},
  { -116.565051177078f,    -78.5095400962685f},
  { -90.0f,    -74.7448812969422f},
  { -135.0f,    -83.2786306606305f},
  { -90.0f,    -80.5376777919744f},
  { -90.0f,    -85.6012946450045f},
  { -85.2363583092738f,    -4.74726225485260f},
  { -79.6951535312340f,    -5.11108969528871f},
  { -73.3007557660064f,    -5.47124945343343f},
  { -66.0375110254218f,    -5.79763632953063f},
  { -57.9946167919165f,    -6.05074601591175f},
  { -49.3987053549955f,    -6.19039945857186f},
  { -40.6012946450045f,    -6.19039945857186f},
  { -32.0053832080835f,    -6.05074601591175f},
  { -23.9624889745782f,    -5.79763632953063f},
  { -16.6992442339936f,    -5.47124945343343f},
  { -10.3048464687660f,    -5.11108969528871f},
  { -4.76364169072618f,    -4.74726225485260f},
  { -84.8055710922652f,    -10.2634278919935f},
  { -78.6900675259798f,    -11.0958032831364f},
  { -71.5650511770780f,    -11.9046881128481f},
  { -63.4349488229220f,    -12.6043826483792f},
  { -54.4623222080256f,    -13.0884760858333f},
  { -45.0f,    -13.2626760083048f},
  { -35.5376777919744f,    -13.0884760858333f},
  { -26.5650511770780f,    -12.6043826483792f},
  { -18.4349488229220f,    -11.9046881128481f},
  { -11.3099324740202f,    -11.0958032831364f},
  { -5.19442890773481f,    -10.2634278919936f},
  { -84.2894068625004f,    -16.6209512676335f},
  { -77.4711922908485f,    -18.0246645268103f},
  { -69.4439547804165f,    -19.3473699609355f},
  { -60.2551187030578f,    -20.4104455216585f},
  { -50.1944289077348f,    -21.0123137896886f},
  { -39.8055710922652f,    -21.0123137896886f},
  { -29.7448812969422f,    -20.4104455216585f},
  { -20.5560452195835f,    -19.3473699609355f},
  { -12.5288077091515f,    -18.0246645268103f},
  { -5.71059313749964f,    -16.6209512676335f},
  { -83.6598082540901f,    -23.8322990618998f},
  { -75.9637565320735f,    -25.8766900608275f},
  { -66.8014094863518f,    -27.7096107852625f},
  { -56.3099324740202f,    -29.0171406246015f},
  { -45.0000000000000f,    -29.4962084965664f},
  { -33.6900675259798f,    -29.0171406246015f},
  { -23.1985905136482f,    -27.7096107852625f},
  { -14.0362434679265f,    -25.8766900608275f},
  { -6.34019174590991f,    -23.8322990618998f},
  { -82.8749836510982f,    -31.8061000193785f},
  { -74.0546040990772f,    -34.4813893719816f},
  { -63.4349488229220f,    -36.6992252004899f},
  { -51.3401917459099f,    -37.9851672993556f},
  { -38.6598082540901f,    -37.9851672993556f},
  { -26.5650511770780f,    -36.6992252004899f},
  { -15.9453959009228f,    -34.4813893719816f},
  { -7.12501634890180f,    -31.8061000193785f},
  { -81.8698976458440f,    -40.3155422107726f},
  { -71.5650511770780f,    -43.4915193450920f},
  { -59.0362434679265f,    -45.8186225388889f},
  { -45.0f,    -46.6861433417170f},
  { -30.9637565320735f,    -45.8186225388889f},
  { -18.4349488229220f,    -43.4915193450920f},
  { -8.13010235415598f,    -40.3155422107726f},
  { -80.5376777919744f,    -49.0104664376223f},
  { -68.1985905136482f,    -52.4285827724619f},
  { -53.1301023541560f,    -54.4623222080256f},
  { -36.8698976458440f,    -54.4623222080256f},
  { -21.8014094863518f,    -52.4285827724619f},
  { -9.46232220802562f,    -49.0104664376223f},
  { -78.6900675259798f,    -57.4874826838300f},
  { -63.4349488229220f,    -60.7940677526006f},
  { -45.0000000000000f,    -62.0616472703976f},
  { -26.5650511770780f,    -60.7940677526006f},
  { -11.3099324740202f,    -57.4874826838300f},
  { -75.9637565320735f,    -65.3864023470214f},
  { -56.3099324740202f,    -68.1681310319003f},
  { -33.6900675259798f,    -68.1681310319003f},
  { -14.0362434679265f,    -65.3864023470214f},
  { -71.5650511770780f,    -72.4515993862077f},
  { -45.0f,    -74.2068309517360f},
  { -18.4349488229220f,    -72.4515993862077f},
  { -63.4349488229220f,    -78.5095400962685f},
  { -26.5650511770780f,    -78.5095400962685f},
  { -45.0000000000000f,    -83.2786306606305f}};
 
/* 3LD geosphere 'oct' [15 0] (902 points) */
const float __geosphere_oct_15_0_dirs_deg[902][2] =
{ { 0.0f,    0.0f},
  { 180.0f,    0.0f},
  { 90.0f,    0.0f},
  { -90.0f,    0.0f},
  { 0.0f,    90.0f},
  { 0.0f,    -90.0f},
  { 0.0f,    4.08561677997488f},
  { 0.0f,    8.74616226255521f},
  { 0.0f,    14.0362434679265f},
  { 0.0f,    19.9831065219000f},
  { 0.0f,    26.5650511770780f},
  { 0.0f,    33.6900675259798f},
  { 0.0f,    41.1859251657097f},
  { 0.0f,    48.8140748342904f},
  { 0.0f,    56.3099324740202f},
  { 0.0f,    63.4349488229220f},
  { 0.0f,    70.0168934781000f},
  { 0.0f,    75.9637565320735f},
  { 0.0f,    81.2538377374448f},
  { 0.0f,    85.9143832200251f},
  { 4.08561677997488f,    0.0f},
  { 4.39870535499553f,    4.38579953077501f},
  { 4.76364169072618f,    9.43022513800569f},
  { 5.19442890773481f,    15.1953712458899f},
  { 5.71059313749964f,    21.7032913642261f},
  { 6.34019174590991f,    28.9056194412282f},
  { 7.12501634890180f,    36.6569329544820f},
  { 8.13010235415598f,    44.7106224551696f},
  { 9.46232220802562f,    52.7526267976188f},
  { 11.3099324740202f,    60.4659427495364f},
  { 14.0362434679265f,    67.5931287950626f},
  { 18.4349488229220f,    73.9611263864812f},
  { 26.5650511770780f,    79.4446195339388f},
  { 45.0000000000000f,    83.7914553738141f},
  { 90.0f,    85.9143832200251f},
  { 8.74616226255521f,    0.0f},
  { 9.46232220802562f,    4.69911946436983f},
  { 10.3048464687660f,    10.1421061565740f},
  { 11.3099324740202f,    16.3925226947094f},
  { 12.5288077091515f,    23.4541373159961f},
  { 14.0362434679265f,    31.2300697755710f},
  { 15.9453959009229f,    39.4940976758250f},
  { 18.4349488229220f,    47.9019378821367f},
  { 21.8014094863518f,    56.0537049722461f},
  { 26.5650511770780f,    63.5770349075918f},
  { 33.6900675259798f,    70.1729713465918f},
  { 45.0000000000000f,    75.5799318935272f},
  { 63.4349488229220f,    79.4446195339389f},
  { 90.0f,    81.2538377374448f},
  { 14.0362434679265f,    0.0f},
  { 15.2551187030578f,    5.01234637696902f},
  { 16.6992442339936f,    10.8445000673424f},
  { 18.4349488229220f,    17.5484006137923f},
  { 20.5560452195835f,    25.0873294286139f},
  { 23.1985905136482f,    33.2861867456403f},
  { 26.5650511770780f,    41.8103148957786f},
  { 30.9637565320735f,    50.2059345082351f},
  { 36.8698976458440f,    57.9946167919165f},
  { 45.0000000000000f,    64.7605981793211f},
  { 56.3099324740202f,    70.1729713465918f},
  { 71.5650511770780f,    73.9611263864812f},
  { 90.0000000000000f,    75.9637565320735f},
  { 19.9831065219000f,    0.0f},
  { 21.8014094863518f,    5.30457143909761f},
  { 23.9624889745782f,    11.4789227189784f},
  { 26.5650511770780f,    18.5419779639972f},
  { 29.7448812969422f,    26.3877999612430f},
  { 33.6900675259798f,    34.7364812812580f},
  { 38.6598082540901f,    43.1384376196711f},
  { 45.0f,    51.0575587310186f},
  { 53.1301023541560f,    57.9946167919165f},
  { 63.4349488229220f,    63.5770349075918f},
  { 75.9637565320735f,    67.5931287950626f},
  { 90.0000000000000f,    70.0168934781000f},
  { 26.5650511770780f,    0.0f},
  { 29.0546040990771f,    5.54765627378992f},
  { 32.0053832080835f,    11.9694631246073f},
  { 35.5376777919744f,    19.2258557454440f},
  { 39.8055710922652f,    27.1191427733811f},
  { 45.0000000000000f,    35.2643896827547f},
  { 51.3401917459099f,    43.1384376196711f},
  { 59.0362434679265f,    50.2059345082351f},
  { 68.1985905136482f,    56.0537049722461f},
  { 78.6900675259798f,    60.4659427495364f},
  { 90.0f,    63.4349488229220f},
  { 33.6900675259798f,    0.0f},
  { 36.8698976458440f,    5.71059313749964f},
  { 40.6012946450045f,    12.2395582977766f},
  { 45.0f,    19.4712206344907f},
  { 50.1944289077348f,    27.1191427733811f},
  { 56.3099324740202f,    34.7364812812580f},
  { 63.4349488229220f,    41.8103148957786f},
  { 71.5650511770780f,    47.9019378821367f},
  { 80.5376777919744f,    52.7526267976188f},
  { 90.0f,    56.3099324740202f},
  { 41.1859251657097f,    0.0f},
  { 45.0f,    5.76818118618822f},
  { 49.3987053549955f,    12.2395582977766f},
  { 54.4623222080256f,    19.2258557454440f},
  { 60.2551187030578f,    26.3877999612430f},
  { 66.8014094863518f,    33.2861867456403f},
  { 74.0546040990772f,    39.4940976758250f},
  { 81.8698976458440f,    44.7106224551696f},
  { 90.0f,    48.8140748342904f},
  { 48.8140748342904f,    0.0f},
  { 53.1301023541560f,    5.71059313749964f},
  { 57.9946167919165f,    11.9694631246073f},
  { 63.4349488229220f,    18.5419779639972f},
  { 69.4439547804165f,    25.0873294286139f},
  { 75.9637565320735f,    31.2300697755710f},
  { 82.8749836510982f,    36.6569329544821f},
  { 90.0f,    41.1859251657097f},
  { 56.3099324740202f,    0.0f},
  { 60.9453959009229f,    5.54765627378992f},
  { 66.0375110254218f,    11.4789227189784f},
  { 71.5650511770780f,    17.5484006137923f},
  { 77.4711922908485f,    23.4541373159961f},
  { 83.6598082540901f,    28.9056194412282f},
  { 90.0000000000000f,    33.6900675259798f},
  { 63.4349488229220f,    0.0f},
  { 68.1985905136482f,    5.30457143909761f},
  { 73.3007557660064f,    10.8445000673424f},
  { 78.6900675259798f,    16.3925226947094f},
  { 84.2894068625004f,    21.7032913642261f},
  { 90.0f,    26.5650511770780f},
  { 70.0168934781000f,    0.0f},
  { 74.7448812969422f,    5.01234637696902f},
  { 79.6951535312340f,    10.1421061565740f},
  { 84.8055710922652f,    15.1953712458899f},
  { 90.0f,    19.9831065219000f},
  { 75.9637565320735f,    0.0f},
  { 80.5376777919744f,    4.69911946436983f},
  { 85.2363583092738f,    9.43022513800569f},
  { 90.0f,    14.0362434679265f},
  { 81.2538377374448f,    0.0f},
  { 85.6012946450045f,    4.38579953077501f},
  { 90.0f,    8.74616226255521f},
  { 85.9143832200251f,    0.0f},
  { 90.0f,    4.08561677997488f},
  { 94.0856167799749f,    0.0f},
  { 94.3987053549955f,    4.38579953077501f},
  { 94.7636416907262f,    9.43022513800569f},
  { 95.1944289077348f,    15.1953712458899f},
  { 95.7105931374996f,    21.7032913642261f},
  { 96.3401917459099f,    28.9056194412282f},
  { 97.1250163489018f,    36.6569329544820f},
  { 98.1301023541560f,    44.7106224551696f},
  { 99.4623222080256f,    52.7526267976188f},
  { 101.309932474020f,    60.4659427495364f},
  { 104.036243467927f,    67.5931287950626f},
  { 108.434948822922f,    73.9611263864812f},
  { 116.565051177078f,    79.4446195339388f},
  { 135.000000000000f,    83.7914553738141f},
  { 180.0f,    85.9143832200251f},
  { 98.7461622625552f,    0.0f},
  { 99.4623222080256f,    4.69911946436983f},
  { 100.304846468766f,    10.1421061565740f},
  { 101.309932474020f,    16.3925226947094f},
  { 102.528807709152f,    23.4541373159961f},
  { 104.036243467927f,    31.2300697755710f},
  { 105.945395900923f,    39.4940976758250f},
  { 108.434948822922f,    47.9019378821367f},
  { 111.801409486352f,    56.0537049722461f},
  { 116.565051177078f,    63.5770349075918f},
  { 123.690067525980f,    70.1729713465918f},
  { 135.0f,    75.5799318935272f},
  { 153.434948822922f,    79.4446195339389f},
  { 180.0f,    81.2538377374448f},
  { 104.036243467927f,    0.0f},
  { 105.255118703058f,    5.01234637696902f},
  { 106.699244233994f,    10.8445000673424f},
  { 108.434948822922f,    17.5484006137923f},
  { 110.556045219583f,    25.0873294286139f},
  { 113.198590513648f,    33.2861867456403f},
  { 116.565051177078f,    41.8103148957786f},
  { 120.963756532074f,    50.2059345082351f},
  { 126.869897645844f,    57.9946167919165f},
  { 135.0f,    64.7605981793211f},
  { 146.309932474020f,    70.1729713465918f},
  { 161.565051177078f,    73.9611263864812f},
  { -180.000000000000f,    75.9637565320735f},
  { 109.983106521900f,    0.0f},
  { 111.801409486352f,    5.30457143909761f},
  { 113.962488974578f,    11.4789227189784f},
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  { -14.0362434679265f,    -31.2300697755710f},
  { -6.34019174590991f,    -28.9056194412281f},
  { -82.8749836510982f,    -36.6569329544821f},
  { -74.0546040990772f,    -39.4940976758250f},
  { -63.4349488229220f,    -41.8103148957786f},
  { -51.3401917459099f,    -43.1384376196711f},
  { -38.6598082540901f,    -43.1384376196711f},
  { -26.5650511770780f,    -41.8103148957786f},
  { -15.9453959009228f,    -39.4940976758250f},
  { -7.12501634890180f,    -36.6569329544821f},
  { -81.8698976458440f,    -44.7106224551696f},
  { -71.5650511770780f,    -47.9019378821367f},
  { -59.0362434679265f,    -50.2059345082351f},
  { -45.0f,    -51.0575587310186f},
  { -30.9637565320735f,    -50.2059345082351f},
  { -18.4349488229220f,    -47.9019378821367f},
  { -8.13010235415598f,    -44.7106224551696f},
  { -80.5376777919744f,    -52.7526267976188f},
  { -68.1985905136482f,    -56.0537049722461f},
  { -53.1301023541560f,    -57.9946167919165f},
  { -36.8698976458440f,    -57.9946167919165f},
  { -21.8014094863518f,    -56.0537049722461f},
  { -9.46232220802563f,    -52.7526267976188f},
  { -78.6900675259798f,    -60.4659427495364f},
  { -63.4349488229220f,    -63.5770349075918f},
  { -45.0000000000000f,    -64.7605981793211f},
  { -26.5650511770780f,    -63.5770349075918f},
  { -11.3099324740202f,    -60.4659427495364f},
  { -75.9637565320735f,    -67.5931287950626f},
  { -56.3099324740202f,    -70.1729713465918f},
  { -33.6900675259798f,    -70.1729713465918f},
  { -14.0362434679265f,    -67.5931287950626f},
  { -71.5650511770780f,    -73.9611263864812f},
  { -45.0f,    -75.5799318935272f},
  { -18.4349488229220f,    -73.9611263864812f},
  { -63.4349488229220f,    -79.4446195339389f},
  { -26.5650511770780f,    -79.4446195339389f},
  { -45.0000000000000f,    -83.7914553738142f}};
 
/* 3LD geosphere 'oct' [16 0] (1026 points) */
const float __geosphere_oct_16_0_dirs_deg[1026][2] =
{ { 0.0f,    0.0f},
  { 180.0f,    0.0f},
  { 90.0f,    0.0f},
  { -90.0f,    0.0f},
  { 0.0f,    90.0f},
  { 0.0f,    -90.0f},
  { 0.0f,    3.81407483429035f},
  { 0.0f,    8.13010235415598f},
  { 0.0f,    12.9946167919165f},
  { 0.0f,    18.4349488229220f},
  { 0.0f,    24.4439547804165f},
  { 0.0f,    30.9637565320735f},
  { 0.0f,    37.8749836510982f},
  { 0.0f,    45.0f},
  { 0.0f,    52.1250163489018f},
  { 0.0f,    59.0362434679265f},
  { 0.0f,    65.5560452195835f},
  { 0.0f,    71.5650511770780f},
  { 0.0f,    77.0053832080835f},
  { 0.0f,    81.8698976458440f},
  { 0.0f,    86.1859251657097f},
  { 3.81407483429035f,    0.0f},
  { 4.08561677997488f,    4.07526902813210f},
  { 4.39870535499553f,    8.72079692816341f},
  { 4.76364169072618f,    13.9896661378727f},
  { 5.19442890773481f,    19.9074988774736f},
  { 5.71059313749964f,    26.4511990993406f},
  { 6.34019174590991f,    33.5280232217311f},
  { 7.12501634890180f,    40.9659247499738f},
  { 8.13010235415598f,    48.5270656910595f},
  { 9.46232220802562f,    55.9467140446854f},
  { 11.3099324740202f,    62.9828767821498f},
  { 14.0362434679265f,    69.4526060024815f},
  { 18.4349488229220f,    75.2368673763685f},
  { 26.5650511770780f,    80.2403277394902f},
  { 45.0000000000000f,    84.2318188138118f},
  { 90.0f,    86.1859251657097f},
  { 8.13010235415598f,    0.0f},
  { 8.74616226255521f,    4.34775315133540f},
  { 9.46232220802562f,    9.33585903200394f},
  { 10.3048464687660f,    15.0202566665138f},
  { 11.3099324740202f,    21.4167140330336f},
  { 12.5288077091515f,    28.4721344245730f},
  { 14.0362434679265f,    36.0398934303039f},
  { 15.9453959009229f,    43.8762651909286f},
  { 18.4349488229220f,    51.6711818985441f},
  { 21.8014094863518f,    59.1057379206062f},
  { 26.5650511770780f,    65.9051574478893f},
  { 33.6900675259798f,    71.8520260682270f},
  { 45.0000000000000f,    76.7373239916952f},
  { 63.4349488229220f,    80.2403277394902f},
  { 90.0f,    81.8698976458440f},
  { 12.9946167919165f,    0.0f},
  { 14.0362434679265f,    4.62203692583713f},
  { 15.2551187030578f,    9.94912629715978f},
  { 16.6992442339936f,    16.0318928587692f},
  { 18.4349488229220f,    22.8620891442349f},
  { 20.5560452195835f,    30.3364156173112f},
  { 23.1985905136482f,    38.2324043541196f},
  { 26.5650511770780f,    46.2194273454749f},
  { 30.9637565320735f,    53.9128529342688f},
  { 36.8698976458440f,    60.9453959009229f},
  { 45.0000000000000f,    67.0102322263912f},
  { 56.3099324740202f,    71.8520260682270f},
  { 71.5650511770780f,    75.2368673763685f},
  { 90.0f,    77.0053832080835f},
  { 18.4349488229220f,    0.0f},
  { 19.9831065219000f,    4.88325044901346f},
  { 21.8014094863518f,    10.5197348906586f},
  { 23.9624889745782f,    16.9409375987462f},
  { 26.5650511770780f,    24.0948425521107f},
  { 29.7448812969422f,    31.8061000193785f},
  { 33.6900675259798f,    39.7621591518051f},
  { 38.6598082540901f,    47.5498444571087f},
  { 45.0f,    54.7356103172453f},
  { 53.1301023541560f,    60.9453959009229f},
  { 63.4349488229220f,    65.9051574478893f},
  { 75.9637565320735f,    69.4526060024815f},
  { 90.0f,    71.5650511770780f},
  { 24.4439547804165f,    0.0f},
  { 26.5650511770780f,    5.11108969528872f},
  { 29.0546040990771f,    10.9932014985969f},
  { 32.0053832080835f,    17.6406309136330f},
  { 35.5376777919744f,    24.9379827032418f},
  { 39.8055710922652f,    32.6267377065311f},
  { 45.0000000000000f,    40.3155422107726f},
  { 51.3401917459099f,    47.5498444571087f},
  { 59.0362434679265f,    53.9128529342688f},
  { 68.1985905136482f,    59.1057379206062f},
  { 78.6900675259798f,    62.9828767821498f},
  { 90.0f,    65.5560452195835f},
  { 30.9637565320735f,    0.0f},
  { 33.6900675259798f,    5.28198245234341f},
  { 36.8698976458440f,    11.3099324740202f},
  { 40.6012946450045f,    18.0246645268103f},
  { 45.0000000000000f,    25.2394018206789f},
  { 50.1944289077348f,    32.6267377065311f},
  { 56.3099324740202f,    39.7621591518051f},
  { 63.4349488229220f,    46.2194273454749f},
  { 71.5650511770780f,    51.6711818985441f},
  { 80.5376777919744f,    55.9467140446854f},
  { 90.0f,    59.0362434679265f},
  { 37.8749836510982f,    0.0f},
  { 41.1859251657097f,    5.37411792901766f},
  { 45.0f,    11.4217536589623f},
  { 49.3987053549955f,    18.0246645268103f},
  { 54.4623222080256f,    24.9379827032418f},
  { 60.2551187030578f,    31.8061000193785f},
  { 66.8014094863518f,    38.2324043541196f},
  { 74.0546040990772f,    43.8762651909286f},
  { 81.8698976458440f,    48.5270656910595f},
  { 90.0f,    52.1250163489018f},
  { 45.0f,    0.0f},
  { 48.8140748342904f,    5.37411792901766f},
  { 53.1301023541560f,    11.3099324740202f},
  { 57.9946167919165f,    17.6406309136330f},
  { 63.4349488229220f,    24.0948425521107f},
  { 69.4439547804165f,    30.3364156173112f},
  { 75.9637565320735f,    36.0398934303039f},
  { 82.8749836510982f,    40.9659247499738f},
  { 90.0f,    45.0f},
  { 52.1250163489018f,    0.0f},
  { 56.3099324740202f,    5.28198245234341f},
  { 60.9453959009229f,    10.9932014985969f},
  { 66.0375110254218f,    16.9409375987462f},
  { 71.5650511770780f,    22.8620891442349f},
  { 77.4711922908485f,    28.4721344245730f},
  { 83.6598082540901f,    33.5280232217311f},
  { 90.0f,    37.8749836510982f},
  { 59.0362434679265f,    0.0f},
  { 63.4349488229220f,    5.11108969528872f},
  { 68.1985905136482f,    10.5197348906586f},
  { 73.3007557660064f,    16.0318928587692f},
  { 78.6900675259798f,    21.4167140330336f},
  { 84.2894068625004f,    26.4511990993406f},
  { 90.0f,    30.9637565320735f},
  { 65.5560452195835f,    0.0f},
  { 70.0168934781000f,    4.88325044901346f},
  { 74.7448812969422f,    9.94912629715978f},
  { 79.6951535312340f,    15.0202566665138f},
  { 84.8055710922652f,    19.9074988774736f},
  { 90.0f,    24.4439547804165f},
  { 71.5650511770780f,    0.0f},
  { 75.9637565320735f,    4.62203692583713f},
  { 80.5376777919744f,    9.33585903200394f},
  { 85.2363583092738f,    13.9896661378727f},
  { 90.0f,    18.4349488229220f},
  { 77.0053832080835f,    0.0f},
  { 81.2538377374448f,    4.34775315133540f},
  { 85.6012946450045f,    8.72079692816341f},
  { 90.0f,    12.9946167919165f},
  { 81.8698976458440f,    0.0f},
  { 85.9143832200251f,    4.07526902813210f},
  { 90.0f,    8.13010235415598f},
  { 86.1859251657097f,    0.0f},
  { 90.0f,    3.81407483429035f},
  { 93.8140748342904f,    0.0f},
  { 94.0856167799749f,    4.07526902813210f},
  { 94.3987053549955f,    8.72079692816341f},
  { 94.7636416907262f,    13.9896661378727f},
  { 95.1944289077348f,    19.9074988774736f},
  { 95.7105931374996f,    26.4511990993406f},
  { 96.3401917459099f,    33.5280232217311f},
  { 97.1250163489018f,    40.9659247499738f},
  { 98.1301023541560f,    48.5270656910595f},
  { 99.4623222080256f,    55.9467140446854f},
  { 101.309932474020f,    62.9828767821498f},
  { 104.036243467927f,    69.4526060024815f},
  { 108.434948822922f,    75.2368673763685f},
  { 116.565051177078f,    80.2403277394902f},
  { 135.0f,    84.2318188138118f},
  { 180.0f,    86.1859251657097f},
  { 98.1301023541560f,    0.0f},
  { 98.7461622625552f,    4.34775315133540f},
  { 99.4623222080256f,    9.33585903200394f},
  { 100.304846468766f,    15.0202566665138f},
  { 101.309932474020f,    21.4167140330336f},
  { 102.528807709152f,    28.4721344245730f},
  { 104.036243467927f,    36.0398934303039f},
  { 105.945395900923f,    43.8762651909286f},
  { 108.434948822922f,    51.6711818985441f},
  { 111.801409486352f,    59.1057379206062f},
  { 116.565051177078f,    65.9051574478893f},
  { 123.690067525980f,    71.8520260682270f},
  { 135.0f,    76.7373239916952f},
  { 153.434948822922f,    80.2403277394902f},
  { 180.0f,    81.8698976458440f},
  { 102.994616791917f,    0.0f},
  { 104.036243467927f,    4.62203692583713f},
  { 105.255118703058f,    9.94912629715978f},
  { 106.699244233994f,    16.0318928587692f},
  { 108.434948822922f,    22.8620891442349f},
  { 110.556045219583f,    30.3364156173112f},
  { 113.198590513648f,    38.2324043541196f},
  { 116.565051177078f,    46.2194273454749f},
  { 120.963756532074f,    53.9128529342687f},
  { 126.869897645844f,    60.9453959009229f},
  { 135.0f,    67.0102322263912f},
  { 146.309932474020f,    71.8520260682270f},
  { 161.565051177078f,    75.2368673763685f},
  { 180.0f,    77.0053832080835f},
  { 108.434948822922f,    0.0f},
  { 109.983106521900f,    4.88325044901346f},
  { 111.801409486352f,    10.5197348906586f},
  { 113.962488974578f,    16.9409375987462f},
  { 116.565051177078f,    24.0948425521107f},
  { 119.744881296942f,    31.8061000193785f},
  { 123.690067525980f,    39.7621591518051f},
  { 128.659808254090f,    47.5498444571087f},
  { 135.0f,    54.7356103172453f},
  { 143.130102354156f,    60.9453959009229f},
  { 153.434948822922f,    65.9051574478893f},
  { 165.963756532074f,    69.4526060024815f},
  { 180.0f,    71.5650511770780f},
  { 114.443954780417f,    0.0f},
  { 116.565051177078f,    5.11108969528872f},
  { 119.054604099077f,    10.9932014985969f},
  { 122.005383208084f,    17.6406309136330f},
  { 125.537677791974f,    24.9379827032418f},
  { 129.805571092265f,    32.6267377065311f},
  { 135.0f,    40.3155422107726f},
  { 141.340191745910f,    47.5498444571087f},
  { 149.036243467926f,    53.9128529342688f},
  { 158.198590513648f,    59.1057379206062f},
  { 168.690067525980f,    62.9828767821498f},
  { 180.0f,    65.5560452195835f},
  { 120.963756532074f,    0.0f},
  { 123.690067525980f,    5.28198245234341f},
  { 126.869897645844f,    11.3099324740202f},
  { 130.601294645005f,    18.0246645268103f},
  { 135.0f,    25.2394018206789f},
  { 140.194428907735f,    32.6267377065311f},
  { 146.309932474020f,    39.7621591518051f},
  { 153.434948822922f,    46.2194273454749f},
  { 161.565051177078f,    51.6711818985441f},
  { 170.537677791974f,    55.9467140446854f},
  { 180.0f,    59.0362434679265f},
  { 127.874983651098f,    0.0f},
  { 131.185925165710f,    5.37411792901766f},
  { 135.0f,    11.4217536589623f},
  { 139.398705354996f,    18.0246645268103f},
  { 144.462322208026f,    24.9379827032418f},
  { 150.255118703058f,    31.8061000193785f},
  { 156.801409486352f,    38.2324043541196f},
  { 164.054604099077f,    43.8762651909286f},
  { 171.869897645844f,    48.5270656910595f},
  { 180.0f,    52.1250163489018f},
  { 135.0f,    0.0f},
  { 138.814074834290f,    5.37411792901766f},
  { 143.130102354156f,    11.3099324740202f},
  { 147.994616791916f,    17.6406309136330f},
  { 153.434948822922f,    24.0948425521107f},
  { 159.443954780417f,    30.3364156173112f},
  { 165.963756532074f,    36.0398934303039f},
  { 172.874983651098f,    40.9659247499738f},
  { 180.0f,    45.0f},
  { 142.125016348902f,    0.0f},
  { 146.309932474020f,    5.28198245234341f},
  { 150.945395900923f,    10.9932014985969f},
  { 156.037511025422f,    16.9409375987462f},
  { 161.565051177078f,    22.8620891442349f},
  { 167.471192290848f,    28.4721344245730f},
  { 173.659808254090f,    33.5280232217311f},
  { 180.0f,    37.8749836510982f},
  { 149.036243467926f,    0.0f},
  { 153.434948822922f,    5.11108969528872f},
  { 158.198590513648f,    10.5197348906586f},
  { 163.300755766006f,    16.0318928587692f},
  { 168.690067525980f,    21.4167140330336f},
  { 174.289406862500f,    26.4511990993406f},
  { 180.0f,    30.9637565320735f},
  { 155.556045219583f,    0.0f},
  { 160.016893478100f,    4.88325044901346f},
  { 164.744881296942f,    9.94912629715978f},
  { 169.695153531234f,    15.0202566665138f},
  { 174.805571092265f,    19.9074988774736f},
  { 180.0f,    24.4439547804165f},
  { 161.565051177078f,    0.0f},
  { 165.963756532074f,    4.62203692583712f},
  { 170.537677791974f,    9.33585903200394f},
  { 175.236358309274f,    13.9896661378727f},
  { 180.0f,    18.4349488229220f},
  { 167.005383208084f,    0.0f},
  { 171.253837737445f,    4.34775315133540f},
  { 175.601294645005f,    8.72079692816341f},
  { 180.0f,    12.9946167919165f},
  { 171.869897645844f,    0.0f},
  { 175.914383220025f,    4.07526902813210f},
  { 180.0f,    8.13010235415598f},
  { 176.185925165710f,    0.0f},
  { 180.0f,    3.81407483429035f},
  { -176.185925165710f,    0.0f},
  { -175.914383220025f,    4.07526902813210f},
  { -175.601294645005f,    8.72079692816341f},
  { -175.236358309274f,    13.9896661378727f},
  { -174.805571092265f,    19.9074988774736f},
  { -174.289406862500f,    26.4511990993406f},
  { -173.659808254090f,    33.5280232217311f},
  { -172.874983651098f,    40.9659247499738f},
  { -171.869897645844f,    48.5270656910595f},
  { -170.537677791974f,    55.9467140446854f},
  { -168.690067525980f,    62.9828767821498f},
  { -165.963756532074f,    69.4526060024815f},
  { -161.565051177078f,    75.2368673763685f},
  { -153.434948822922f,    80.2403277394902f},
  { -135.0f,    84.2318188138118f},
  { -90.0f,    86.1859251657097f},
  { -171.869897645844f,    0.0f},
  { -171.253837737445f,    4.34775315133540f},
  { -170.537677791974f,    9.33585903200394f},
  { -169.695153531234f,    15.0202566665138f},
  { -168.690067525980f,    21.4167140330336f},
  { -167.471192290848f,    28.4721344245730f},
  { -165.963756532074f,    36.0398934303039f},
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  { -33.6900675259798f,    -39.7621591518051f},
  { -23.1985905136482f,    -38.2324043541196f},
  { -14.0362434679265f,    -36.0398934303039f},
  { -6.34019174590991f,    -33.5280232217311f},
  { -82.8749836510982f,    -40.9659247499738f},
  { -74.0546040990772f,    -43.8762651909286f},
  { -63.4349488229220f,    -46.2194273454749f},
  { -51.3401917459099f,    -47.5498444571087f},
  { -38.6598082540901f,    -47.5498444571087f},
  { -26.5650511770780f,    -46.2194273454749f},
  { -15.9453959009229f,    -43.8762651909286f},
  { -7.12501634890180f,    -40.9659247499738f},
  { -81.8698976458440f,    -48.5270656910595f},
  { -71.5650511770780f,    -51.6711818985441f},
  { -59.0362434679265f,    -53.9128529342688f},
  { -45.0f,    -54.7356103172453f},
  { -30.9637565320735f,    -53.9128529342688f},
  { -18.4349488229220f,    -51.6711818985441f},
  { -8.13010235415598f,    -48.5270656910595f},
  { -80.5376777919744f,    -55.9467140446854f},
  { -68.1985905136482f,    -59.1057379206062f},
  { -53.1301023541560f,    -60.9453959009229f},
  { -36.8698976458440f,    -60.9453959009229f},
  { -21.8014094863518f,    -59.1057379206062f},
  { -9.46232220802562f,    -55.9467140446854f},
  { -78.6900675259798f,    -62.9828767821498f},
  { -63.4349488229220f,    -65.9051574478893f},
  { -45.0000000000000f,    -67.0102322263912f},
  { -26.5650511770780f,    -65.9051574478893f},
  { -11.3099324740202f,    -62.9828767821498f},
  { -75.9637565320735f,    -69.4526060024815f},
  { -56.3099324740202f,    -71.8520260682270f},
  { -33.6900675259798f,    -71.8520260682270f},
  { -14.0362434679265f,    -69.4526060024815f},
  { -71.5650511770780f,    -75.2368673763685f},
  { -45.0000000000000f,    -76.7373239916952f},
  { -18.4349488229220f,    -75.2368673763685f},
  { -63.4349488229220f,    -80.2403277394902f},
  { -26.5650511770780f,    -80.2403277394902f},
  { -45.0000000000000f,    -84.2318188138118f}};
 
/* 3LD 'ico' geosphere arrangements HANDLES */
const float* __HANDLES_geosphere_ico_dirs_deg[17] =
{ &__geosphere_ico_0_0_dirs_deg[0][0],
  &__geosphere_ico_1_0_dirs_deg[0][0],
  &__geosphere_ico_2_0_dirs_deg[0][0],
  &__geosphere_ico_3_0_dirs_deg[0][0],
  &__geosphere_ico_4_0_dirs_deg[0][0],
  &__geosphere_ico_5_0_dirs_deg[0][0],
  &__geosphere_ico_6_0_dirs_deg[0][0],
  &__geosphere_ico_7_0_dirs_deg[0][0],
  &__geosphere_ico_8_0_dirs_deg[0][0],
  &__geosphere_ico_9_0_dirs_deg[0][0],
  &__geosphere_ico_10_0_dirs_deg[0][0],
  &__geosphere_ico_11_0_dirs_deg[0][0],
  &__geosphere_ico_12_0_dirs_deg[0][0],
  &__geosphere_ico_13_0_dirs_deg[0][0],
  &__geosphere_ico_14_0_dirs_deg[0][0],
  &__geosphere_ico_15_0_dirs_deg[0][0],
  &__geosphere_ico_16_0_dirs_deg[0][0]};
 
/* 3LD 'oct' geosphere arrangements HANDLES */
const float* __HANDLES_geosphere_oct_dirs_deg[17] =
{ &__geosphere_oct_0_0_dirs_deg[0][0],
  &__geosphere_oct_1_0_dirs_deg[0][0],
  &__geosphere_oct_2_0_dirs_deg[0][0],
  &__geosphere_oct_3_0_dirs_deg[0][0],
  &__geosphere_oct_4_0_dirs_deg[0][0],
  &__geosphere_oct_5_0_dirs_deg[0][0],
  &__geosphere_oct_6_0_dirs_deg[0][0],
  &__geosphere_oct_7_0_dirs_deg[0][0],
  &__geosphere_oct_8_0_dirs_deg[0][0],
  &__geosphere_oct_9_0_dirs_deg[0][0],
  &__geosphere_oct_10_0_dirs_deg[0][0],
  &__geosphere_oct_11_0_dirs_deg[0][0],
  &__geosphere_oct_12_0_dirs_deg[0][0],
  &__geosphere_oct_13_0_dirs_deg[0][0],
  &__geosphere_oct_14_0_dirs_deg[0][0],
  &__geosphere_oct_15_0_dirs_deg[0][0],
  &__geosphere_oct_16_0_dirs_deg[0][0]};
 
/* Number of points in each 'ico' geosphere arrangement */
const int __geosphere_ico_nPoints[17] =
{   12, 32, 42, 92, 162, 252, 362, 492, 642, 812, 1002, 1212, 1442, 1692, 1962, 2252, 2562   };
 
/* Number of points in each 'oct' geosphere arrangement */
const int __geosphere_oct_nPoints[17] =
{   6, 14, 18, 38, 66, 102, 146, 198, 258, 326, 402, 486, 578, 678, 786, 902, 1026   };